Turner was born in Ellesmere Port and was an England youth international. He started his playing career at Wrexham before moving to rivals Chester in January 1968 in part-exchange for Ian Moir. Five years and 218 Football League appearances later he moved to his third and final club Shrewsbury Town for £30,000. Having played as a midfielder for his first two clubs, he switched to centre back. He went on to make over 350 league appearances for the Salopians. During the 1970s he played against Hereford United several times, the club he was later to buy.

He became player-manager for the Shrews in the 1978–79 season, the same year the club sealed the Third Division championship. Shrewsbury ultimately spent ten seasons in the Second Division and Turner twice led them to the quarter-finals of the FA Cup. He ended his playing career in 1983, and left Shrewsbury after six seasons to take charge of Aston Villa in the summer of 1984.

Unfortunately for Turner, his time at Villa Park was less successful and he was sacked on 14 September 1986, just over two years after his appointment, as Villa were heading for relegation from the First Division.

He was then appointed manager of Wolverhampton Wanderers, a club then in the Fourth Division and massively in financial trouble (barely out of debt), on 7 October 1986. In his first season Wolves reached the play-offs but failed to secure promotion. However the following two seasons brought successive landslide promotions with the help of goal-machine Steve Bull and striking partner Andy Mutch. Mid-table finishes in the Second Division, and subsequently (following the formation of the Premier League) Division One, followed before he left in March 1994. There had been speculation about his future as manager more than two years earlier after a dismal start to the 1991–92 season, but a turnaround in form preserved his job for a while.

He was appointed manager of Hereford United for the start of the 1995–96 season, then in Division Three. His first season was a success, reaching the FA Cup Third Round and the play-offs, losing over two legs to Darlington. But the club was in financial trouble before his arrival and he was unable to retain several key players for the following season. On 3 May 1997, Hereford were relegated to the Conference in a traumatic 1–1 draw with Brighton. Having seen his resignation rejected he oversaw a sixth-place finish in the Conference and, when chairman Peter Hill resigned, he purchased the majority shareholding in the club in partnership with Joan Fennessy — thus saving it from going under.

2002–03 proved the turning point with Turner taking the opportunity to build an entirely new squad, retaining only six players from the previous season. The team, built entirely of free transfers, evolved into arguably the best footballing side in the Conference, finishing second in a record-breaking 2003–04 season. But Hereford faltered in the play-off semi final against Aldershot Town, with crucial decisions going against them. Another runners-up spot and play-off failure came the following season but the 2005–06 season proved third time lucky when Hereford defeated Halifax Town in the 2006 Conference Playoff Final, to secure promotion to the Football League. After the match, Turner said his overwhelming feeling was “relief” after many hard seasons in the Conference. Hereford survived their first season back in the Football League in 16th position. The 2007–08 saw Turner make full use of the loan system, without paying any transfer fees. The Bulls placed consistently in the top 5 all season and achieved promotion to the league’s third tier for the first time in 30 years.

Having finally gained the promotion he had come close to in 1995–96, Turner again used the loan system in League One, purchasing only one player for an undisclosed fee. However this strategy was not nearly as successful in 2008–09 as the Bulls struggled in League One and were relegated on 18 April 2009. Turner subsequently announced he was stepping down as manager, having apologised for the season’s performance. On 24 April 2009, as chairman, he appointed John Trewick as his successor.

Turner remained chairman, director of football and majority shareholder of Hereford United until the end of the 2009–2010 season. His time in charge saw him stabilise the club’s finances, turning a profit for the last six seasons,. In his near 14 season spell at Hereford he purchased just three players: Neil Grayson (£20,000 in 1997), Ben Smith (£20,000 in 2007) and Matt Done (undisclosed in 2008) although Toumani Diagouraga arrived on a permanent transfer as part of the sale of Lionel Ainsworth to Watford. On 8 March 2010 Hereford United announced that they had sacked John Trewick with Turner taking the reins on a temporary basis.

On 16 April 2010 Turner stated that he and co-chairperson Joan Fennessy would sell their shares in the club, stating that the club needs fresh impetus to take it forward. His subsequent decision to return to Shrewsbury Town seems to have influenced his decision.

On 11 June 2010, Turner was announced as the new Shrewsbury Town manager, returning 26 years after he originally left. Turner agreed a three-year-deal as manager, and will have the option of an extra year as director of football. His first season back at Shrewsbury Town was during the 2010–2011 season saw them finish just below automatic promotion in fourth place, this meant that Town had to play a two legged play-off semi final against Torquay United in which they lost 2–0 on aggregate. The following season saw an even greater improvement guiding Shrewsbury Town to a runners-up spot and automatic promotion to League One. The club set a record number of points and for the second time in Turner’s career he led Shrewsbury Town unbeaten at home throughout a whole season 33 years after the first achievement.

In October 2010, Graham received an award from the City of Hereford giving him Freedom of the city.

After guiding them to a respectable 16th-place finish in the 2012/13 season, their first 3rd tier appearance in 15 years, Turner was unable to build on this success the following season. On 21 January 2014 Graham Turner resigned as manager of Shrewsbury Town, halfway through the 2013/14 campaign. Shrewsbury were subsequently relegated.