The 36-year-old and Pitt, 48, confirmed their engagement news recently. Jeweler Robert Procop, who designed the bauble, first broke the news about couple's engagement.
Jolie was first seen wearing the sparkling diamond at the Los Angeles County Museum of Art's Chinese Galleries.
But Jolie took the band off for her recent meeting with the foreign minister of Ecuador and now Showbizspy reports that the actress is not very fond of the ring.
"She isn't fond of it. Nothing against Brad's design. She's just never been enamored of white diamonds. Emeralds are her favorite. The diamond shows how little he knows her. She's so demanding. She's acting like a bridezilla," a friend said.
The actress became romantically involved with Pitt, who was then married to Jennifer Aniston, after they worked together in "Mr and Mrs Smith".
The Hollywood couple has three adopted children, Maddox, Pax, and Zahara, and three biological children, Shiloh, Knox, and Vivienne.