Some cats don't like the enclosure. In the wild, when the eliminate, it's a vulnerable position to be in. I bet if you took the top off, he'd be better at going in the box as he can see all around him. 

My cat does this like once a month but it's not habitual. I think she just...misses? Ever so slightly off the edge. (Some pre-clean up if you can't stomach it immediately, sprinkle with baking soda to try it out and adsorb some of that smell.)
 

I have had cats that hate the cover though. 

I don't really have any advice, but you reminded me of a cat we had when I was a kid. He would carefully dig a hole in the litter, then turn around the wrong way and poop on the floor. Every day. For years. He also routinely ran into a big upright piano. 

I really hope your cat gets over his problem. Like others said, try a different litter pan or maybe a different litter?

Thanks! He does usually go in the box and dig in it...and then turn around and poop outside of it! I could scream sometimes.

our old guy started doing that then peeing outside too. that was about it for him he was pretty much worn out. 

Keep your chin up! Hopefully yours is smarter than ours was. Ours was just a big old mama's boy. He never even washed himself!

Our sweet Maine Coon was a big boy, and would do exactly the same thing. He always peed in his box with no problem, but I'd wake up every morning to a little gift left in front of the bathroom sink. 

We bought a huge litter box with high sides and back, and filled it fuller than normal with litter. It turned out he liked to circle, dig, and circle some more before settling down to business. It really helped, and although he still gifted us on occasion, it was drastically reduced.