Graham was quoted in a QRU statement as saying: "I'm naturally disappointed.
"I loved my role with the Reds and enjoyed my time with the QRU.
"I am in a high-performance environment and the results haven't been to a satisfactory standard. I have to accept that and move on.
"I wish everybody the best and want to formally thank the competent and dedicated support staff I have worked with over the last three years for their tireless efforts.
"I really hope the team and Reds coaching staff have success going forward."
QRU chairman Damien Frawley said: "I'd like to thank Richard for his contribution over the past number of years.
"Richard is a proud Queenslander who has spent his life in Rugby and while he hasn't achieved the success we all would have wished for during his time as head coach, he leaves with our gratitude for his service to the game."
"QRU conducted a high-performance review in the middle of last year and as a result implemented significant change across our rugby department.
"At that time the board made the decision to reappoint Richard as head coach for a year, but we always said there would be periods within the 2016 Super Rugby season where we would take stock of how the team was performing."
- AAP