Mr. Ping's grandfather is a Chinese goose who was father to Mr. Ping's father (thus making him grandfather to Mr. Ping), and adoptive great-grandfather to Po. He was one of the previous owners of the Noodle Shop, although his name was never specified.
However, it is known that he was the one to win the Noodle Shop from one of his friends (the first known owner of the shop) in a game of mahjong. He started the family business of serving noodles to the villagers of the Valley of Peace, and thus also may be the creator of the so-called "secret ingredient" of the noodle soup—revealed in the first film to be nothing but the mere belief of the soup being special. The "secret ingredient" was kept as a family secret for each generation before him, usually being revealed to family members after they had had the "noodle dream"—a dream signifying their family member's destiny to take over the restaurant.
It is assumed that Mr. Ping's grandfather had his son, Mr. Ping's father, take over the Noodle Shop—presumably after having the "Noodle Dream" and being told the "secret ingredient" of the noodle soup.
Since neither of them make a direct appearance, their relationship is unknown.
Mr Ping's relationship with his grandfather is unknown, but he keeps a picture of him in his kitchen.
He's shown wearing a bowl of noodles as a hat and wearing a brown shirt, which can be partially seen.