Terrell Talley today said his girlfriend China Arnold had admitted to killing the one-month-old girl, named Paris.
The girl was pronounced dead in August 2005, after the couple took her to hospital.
Some months later, in a phone conversation, Talley said Arnold told him of a possible motive for her actions.
"She told me if I wouldn't be out cheating, my baby would still be alive," Talley told the court.
Arnold has pleaded not guilty to aggravated murder and could face the death penalty if convicted.
Under questioning by defence lawyer Jon Paul Rion, Talley acknowledged telling people he did not have any idea what happened to the baby.
The defence has said that people other than Arnold had access to the baby and that she was intoxicated when the baby died.
Talley said Arnold was drunk, but not so drunk that she would not know what happened.
He said the baby was fine when he went to sleep.
But the next morning, Talley said he saw a red mark on the baby's face and noticed she was stiff and cold.
The trial continues.