The 35-year-old driver who resides at Dobson Land, Black Rock, St Michael, pleaded guilty to assaulting Tanya Best and occasioning her actual bodily harm.
According to acting Station Sergeant Neville Watson, Best and Babb have a son together. The woman ended the relationship and told Babb he could continue seeing the child.
On May 26, while she and the baby were at a bus stop, Babb attempted to take the child from the stroller but the woman blocked him. Babb then pushed her to the ground where she hit and bruised the left side of her face.
Others at the bus stop held on to Babb and the police were called. Babb later admitted to police that he committed the offence.
He returns to court before Magistrate Douglas Frederick on Friday, when the complainant is expected to attend and compensation determined.
Bail was granted at $2 500 with one surety.