Benjamin Cole, 57, was given a lethal injection at McAllister Prison in the central United States, according to prison officials.
Cole was sentenced to death in 2004 for the murder of his nine-month-old daughter.
The prosecution admitted at the time that he killed her to silence her before returning to playing a video game.
His lawyers indicated that he had long suffered from “paranoid schizophrenia” and brain damage.
The US Supreme Court has banned the execution of inmates who do not understand the reason for their conviction.
As the date of his execution approached, defenders of his cause redoubled their appeals to try to save him, but their action yielded no positive results.
Oklahoma authorities justified his execution by saying that a doctor had confirmed that nothing stood in the way of his execution.
During his execution, Benjamin Cole prayed loudly and incomprehensibly, according to local reporters who attended as witnesses.
And the Cole’s execution is the twelfth execution this year in the United States and the fourth in the state of Oklahoma, which has re-set the date of several executions in the coming months after being halted over doubts about the legitimacy of the injection.