The `Wild Horses` singer has been hounded by the man, who has managed to get her phone number and claims to be relative, and now her family are terrified something serious is going to happen.
Her brother Gerry told the News of the World newspaper: "He is calling Susan and pretending to be me or other relatives. It`s been going on for a while. Susan knows who I am when I get on the phone. She never mistakes me for him.
"There are some weird people around. But this one is stalking her and has got her number. It is serious. Stalkers can become dangerous."
Although Susan, 49, insists she doesn`t need any more protection, Gerry feels her security should be increased.
He said: "Susan knows having stalkers goes with the territory. She`s massively well known so having people interested in her is going to happen. It`s down to her management to work it out for her. How has someone been able to contact her?
"Our family have very serious reservations about whether she has enough security at the moment. She needs protection or it`s a matter of time."
Last year, Susan was "shaken-up" after a stalker turned up at her home.
The star was bombarded with strange letters from a US woman, who went to her home in West Lothian, Scotland.
A source said: "This woman is constantly following Susan around the world. It is a middle-aged American woman who has become obsessed with her."