The composite sketch shows that the suspect, dubbed as the "Ear Gauge Stalker," has distinct earlobe gauge piercings.
Police said he groped one woman who was pushing a baby stroller, but ran away when she screamed. The suspect grabbed another woman, dragged her to a secluded area and tried to undress her before two passersby scared him off.
The attacks happened last Sunday at the Mountain View Manor apartments on Dronfield Avenue.
"The suspect's bold behavior speaks to someone who is impulsive and probably compulsive," said Lt. Paul Vernon with the Los Angeles Police Department.
The suspect was described as a medium-build African American man in his mid-20s, standing 5 feet 8 inches tall and weighing 160 pounds.
Anyone with information was urged to call Los Angeles Regional Crime Stoppers at 1-800-222-TIPS.