The Invisible Man is the most exciting character in the book. Even if we don't like him, he's certainly the most active character and we're easily drawn into his adventures. (He's the one who sets these adventures into motion, after all.) He's kind of like Jay Gatsby from The Great Gatsby. He's the center of attention for all the characters and a mystery that we want to solve. Plus he's the most tragic figure in the book – if you hadn't noticed, not much goes well for this guy.
The Invisible Man? Protagonist? Really? Yeah, we have some reservations, too. Our other option for a protagonist would be Dr. Kemp, the character that leads the opposition to Griffin. The thing is, Kemp really can't be the protagonist of The Invisible Man because he shows up when the novel is more than halfway over. But let's see what kinds of protagonist-like characteristics he has.
He is a much more likeable character than the Invisible Man, that's for sure. More importantly, he reacts to the Invisible Man's story in a way that many readers probably react (i.e. like a normal person with a heart who doesn't think bashing in people's heads is morally acceptable). This helps us identify with him, which is majorly important for a protagonist (sorry, Invisible Man). Let's put it this way: The Invisible Man would be a much more palatable story if Kemp were our protagonist. Instead, we're supposed to be rooting with a psychopathic killer? No, thank you.