I don't understand it, it's as if the man has no life at all. When you see him, all he talks about is the Hulk. I am watching this series so far, he has faced the Hulk in some episodes, and he has done nothing. If he captures the Hulk, does he get a reward from the newspaper company he works for? Because many of his colleagues don't believe in the Hulk.

Jack McGee explained his intentions succinctly in the pilot episode. After
the service ended, he was walking from the cemetery with Ben, a friend of
Elaina Marks and David Banner from the Institute.

BEN: .. You actually saw the thing that killed them both?
McGEE: Yeah -- just before the lab exploded with Banner inside; I've given
its description to all the law-enforcement agencies. There's a warrant for
murder out on it. Believe me, something that looks like that Hulk
isn't going to stay hidden very long -- and when it's captured, it's going to be
one of the great stories of the twentieth century!

I don't think McGee ever stopped believing the Hulk was a killer ... even after
he saved his life a number of times. Still, he learned something in "Mystery
Man," that the Hulk was a man (his "John Doe") who turned into the creature;
and, in "Prometheus," in which Banner was trapped in halfway transformation,
McGee may have felt a little bit of compassion. I would like to have seen
some closure in "The Death of the Incredible Hulk"; but, unfortunately (for
whatever reason), actor Jack Colvin does not appear in that final TV-movie.

I don't understand it, it's as if the man has no life at all.

The Hulk IS his life:)