You say "He's going home," never "He's going to home." You could say "He's going to my home," or "He's going to his home," as well. You would not say "He's going my home," or "He's going his home."

Sorry for my mistake, he's going to go home :)

Going home. I never ever heard anyone saying going TO home... unless the sentence is "going to home-page" :D

I think both sentences are right. But different meaning. First one is present continuous, other is simple future. ''He's going home" means he is on the way to home. And He's going to home means He will definitely go home.