Mary, Stella, James and step-daughter Heather are all extremely concerned about the former Beatle's upcoming concert in Israel after he received murderous warnings from Islamic extremist Omar Bakri Muhammad.
The star was branded an "enemy" of all Muslims for his decision to perform in the Jewish country, but 66-year-old Paul has dismissed the threats.
A family source said: "Paul's family know he's not the type to back down but that doesn't stop them being extremely worried about him."
"It's understood his kids would prefer him not to do the show but they also accept their dad will do what he believes to be right and won't be scared off."
The music legend is due to perform at the Friendship First concert, which marks Israel's 60th anniversary, later this month.
Hate preacher Bakri has revealed there are martyrs prepared to give up their lives in order to kill Paul.
Bakri was quoted as saying: "Our enemy's friend is our enemy. We have what we call 'sacrifice' operatives who will not stand by while he joins in a celebration of their oppressions. If he values his life Mr. McCartney must not come to Israel."
Speaking on a TV show about the possible assassination attempt, Paul said: "I was approached by different political bodies who asked me not to come here. I refused. I do what I think and I have many friends who support Israel."
