He used to take his son Goofy on road trips to go fishing in Lake Destiny. In A Goofy Movie, Goofy decides to take his own son, Max on the same route, as a family tradition.
In the Island in the Sky, Goofy briefly mentions his parents when he waves goodbye to his loved ones. Both characters, however, remained unseen.
In the episode The Adventure Story, which first aired on March 20, 1957, Goofy tells his son Junior about their ancestors and relatives. The Goofy cartoons Tiger Trouble and African Diary were featured in this episode, and it was said that the goofy from these cartoons was in fact named Amos Goofy, and that he was Junior's grandfather and Goofy's father. In later printings of the comic adaptation of this episode, Amos was renamed Hunter Goofy.
In the House of Mouse episode "Goofy's Menu Magic", when Goofy says he's working on some popcorn, he can be heard saying: "How's the corn comin', pop?". We then see Goofy's father peeling corn in the kitchen.
In the Goof Troop episode "Clan of the Cave Goof", Max's grandpa (presumably Goofy's father) is mentioned when Max tries to use the argument of "Grandpa never went to the dentist," to get out of going to his own dentist appointment, to which Goofy responds "Grandpa doesn't have any teeth, Maxie."
When Goofy decides to take Max on a fishing trip to Lake Destiny, Idaho in A Goofy Movie, he tells Max that they will use the same map he and his own dad used when they went on the same fishing trip back when Goofy was Max's age. When Goofy unfolds the map, the map is shown to have previously belonged to first a "Walter P. Goofey", then a "Benjamin Goofey", and finally "all Goofeys", with the name "Benjamin Goofey" possibly being the name of Goofy's father (or at least one of Goofy's relatives). Later in the movie, Goofy tells Max that his (Max's) granddad had taught Goofy how to open up a soup can with his teeth back when Goofy and his dad had taken a trip to Yosemite together.
When Max goes off to college in An Extremely Goofy Movie, Goofy gives him his father's old adding machine as a gift.