The name Ojisan means either uncle, grandpa, or old man. Ojisan is probably Chuko's grandfather. Ojisan is a slightly skinny old man with puffy white hair and mustache and he has black eyes. He wears a shirt and vest and pants with patches along with plain brown shoes. He looks a lot like, or is at least stylized a lot like Gepetto from Disney's Pinnochio. (Osamu Tezuka who originally wrote and drew the story of Unico, was a HUGE Walt Disney fan, and it can be seen especially in this movie which was based off one of his original Unico manga stories.)
Ojisan takes care of Chiko and is constantly caring for her, worring about her and is often in the depths of despair. Ojisan seems to rarely smile because of his worries, but it is evident that he and Chiko love each other dearly. Chiko's parents are never seen in the film, and it can probably be assumed that they are probably dead for unknown reasons (maybe because of the pollution) and now Ojisan seems to be Chiko's only parent figure and family.
Ojisan is not a mean parent at all, but since he worries about Chiko's health, he throws Unico out of the house, either telling Chiko she can't have a pet because they are hazardous to her health of since they don't know what Unico is. However, when Chiko goes after Unico and collaspes outside, when she wakes up, Ojisan has let Unico back into the house and lets her keep him with a warm chuckle. He lets Chiko keep him, since he realizes how much Chiko likes him. Also, Unico probably alerted him about Chiko fainting outside, because he probably didn't know she was even out there.