The 36-year-old rapper had his first child with the reality TV star on June 15 and wants to capture every moment of his girls spending time together.
A source told HollywoodLife.com: ''He loves taking pictures and videos of Kim and the baby. He's making memories of his fresh new family. They're in the moment and want every minute of it to themselves.''
Kim has been keeping a low profile since becoming a mum, spending most of her time at home to respect Kanye's wish to keep their baby daughter out of the spotlight, even though she wants to show the world how beautiful North is.
Kanye - known for his wild outbursts - is also being cautious and worries he will become irrational if he feels North is in danger from the prying eyes of the public.
The source added: ''[Kanye] is really scared about how he would react if something happened to his baby with someone trying to invade his privacy on the streets.''
The trio have been staying with Kim's mum and manager Kris Jenner since the birth as their new home is still undergoing renovation.
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