Sam Cook Penny is his niece in the comics. She's his daughter in the show. But still, it's not right.
Licha Thanks to everyone for their thoughts. I'm sorry I didn't originally see some of the responses.
This answer contains spoilers… (view spoiler)[He is obsessed with his daughter. She is the last remnant of his previous life. He pulled her teeth out so he could safely kiss her. Perhaps this attempt at affection might grow into a warped sexual relationship with her. We have seen what he did to Michonne when she was his captive. (hide spoiler)]
This answer contains spoilers… (view spoiler)[In a firefight with a group early on, the Governor's daughter is shot and killed. The Governor refuses to kill his now walker-turned daughter. Following his moving into and taking over of Woodbury, he keeps Penny restrained in his apartment, feeding her body parts of the deceased. (hide spoiler)]