The stalker is claiming to be a relative of SuBo’s and wants to meet her.
The singer’s family is worried that something dreadful will happen if this isn’t contained.
Susan’s brother Gerry, 55, said he worries for his sister and her safety.
"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."
He added: "There are some weird people around. But this one is stalking her and has got her number. It is serious. Stalkers can become dangerous."
"Susan knows having stalkers goes with the territory," he said.
"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."
Gerry added: "Mark Chapman killed John Lennon because he knew he was an easy target with no security. That's the same as Susan right now. I've been telling them that for ages. It is scary."
Everyone feels extra security for SuBo would be best.
A source close to Simon Cowell said: "Simon has always wanted the best security for Susan. If there is concern for her safety because of a stalker, he would encourage everyone to ensure it is resolved."