The 23-year-old star, whose mother is the late Paula Yates, says her father just can't get enough of two-month-old Astala and she thinks it's because he finally has a boy in the family, reported Hello magazine.
"He was incredibly gentle with Astala; he took him aside and was so quiet, which isn't something my dad's renowned for. He's besotted with Astala because he's his first grandchild but especially, I think, because he's the first boy in the family," she said.
Besides Peaches, Bob has three other daughters Fifi, 29, Pixie, 21, and 15-year-old Heavenly, who he adopted after the deaths of her parents, Bob's ex-wife Paula and her lover Michael Hutchence.
Peaches says her father's phone screensaver is a picture of Astala, her child with her musician fiance Thomas Cohen.