Keon Deshez Leverett, 19, of 213 E. Hale St., is being sought in connection with the homicide.
Warrants have been filed against Leverett for murder, armed robbery and possession of a firearm during the commission of a crime, according to Lt. Calvin Chew, of the Richmond County Sheriff's Office.
Witnesses heard two or three shots about 4 p.m. in the 300 block of Sterling Street and saw Tolbert, 47, run out of a house and collapse, police said.
Anyone with information on Leverett's whereabouts is asked to contact the s heriff's office at (706) 821-1080.
It is the county's 31st homicide of the year.