A 42-year-old woman who was followed home from a supermarket saw the same man knocking on her window two days later and then trying to get into her home a week after that, police said.
Met detectives are investigating an allegation of harassment and have released a CCTV image of a man they would like to speak to.
The woman was followed from a supermarket on Durnsford Road to her home in Wimbledon, south west London, at 10.50pm on October 26.
Two days later, at around the same time, she heard knocking on her front window and saw the same man staring at her through the glass.
He was then seen in her back garden, trying to get into her home, on the evening of November 5.
The man is described as white, in his 20s, and 6ft tall with a shaved head.
He is believed to have a scar on the left side of his head. During the first incident he was seen wearing a black puffer jacket and dark trousers.
Anyone who recognises this man, or who has any information, is asked to contact Merton police on 101, quoting image 194308. Alternatively, they can contact Crimestoppers anonymously on 0800 555 111.