Sounds like a training issue. Lower the jumps and do more flat work. Grid work is really good for stopping a rusher as it makes them think and requires them to think of where they put their feet. Do you have any videos of you jumping?
Definitely make sure that you have all of your problems fixed on the flat and then over ground polls. Make sure you are nice and relaxed when you are jumping so you don't hype up your horse. Introduce one small cross rail and work on bending before and after the jump. Also make sure he will half halt before and after nicely so you know he is responsive.
Unfortunately your horse doesn't have as much training as you think, running at jumps and over jumping are big big indicators of a greenie over fences. Did YOU train him to jump, or did this "training" come with your horse? Are you currently working with a trainer, and how high are you jumping? Are you jumping lines, courses or single fences?
It's hard to help if we don't have answers to the above- right off the bat I'd recommend lots of circles, lots of trotting to jumps and trotting away, halting after the fences, grid work, cross rails, heck start at poles on the ground and start moving back up again.