The suspect allegedly offered her sweets and then chased her home in Wandsworth.
He grabbed the girl by the hair before she got inside her house on Dover Park Drive.
The man started chatting to her after they met at a bus stop in November 2018.
Cops have now released a CCTV still of the suspect.
He is described as a tall black male, wearing dark clothing at the time of the incident.
The Metropolitan Police said in a statement: “He started a conversation and tried to convince her to come home with him, promising her sweets if she did so.
“She refused and ran away but was chased down the road by the man until she reached her address.
“As she neared the building, the suspect grabbed her by the hair but she managed to get inside and close the door behind her, stopping him from entering.”
Detectives from the Met’s South West CID added: “While incidents like this are rare we are very keen to trace this man and would urge anyone who can identify him to come forward.
“Anyone with information should call 101 with CAD reference 5937/02NOV.”