If your horse has a short, choppy trot, chances are he's on the forehand. Some horses have a naturally short, choppy stride, as someone mentioned about a steep shoulder/pastern angle can contribute to this.
Bending and stretching is the key here. You need to get this horse off the forehand and supple through the body to allow him to open his shoulder, thus lengthening his stride.
First of all check that your saddle is not pinching anywhere, and that it is not sitting on his shoulders. A saddle on a horses shoulders is like you trying to walk with your thighs tied together!!
You should start with riding multiple walk-trot-walk and canter-trot-canter transitions, changing rein (figure of 8's, serpentines and shallow loops will help immensely) and spiralling in and out on a 20m circle using leg yield. These will all help to open his shoulders, relax his back and allow his hinds to swing through, thus opening his stride.
It is most definately NOT a case of just making him run faster and faster, that is simply putting him further onto the forehand and teaching him to be heavy in the hand and brace his back.