The Labour MP, 64, says he has suffered “extensive periods of ill health” and does not feel he will be able to serve for another five years.
Graham, who was first elected in 1987, called it the “hardest decision” of his life.
“I have suffered extended periods of ill health this year with more expected,” he wrote in a letter to his Nottingham North constituents.
“I would have enthusiastically completed the rest of the Parliament to 2020.
“However, the certainty of continuing at the pace and standards that I set myself for a further full five-year term cannot be guaranteed.”