How close are we talking? 2-6 feet?
If that's the case, there are several things you can do to improve.
1. Don't give the hole away. Very few short putts break enough to justify aiming outside the hole.
2. Follow through
3. Pretend that you already made it, and results don't matter anymore.
4. Last but not least! (insert drumroll here)
Lay your putter down on the practice green. Poke 2 tees into the green, one at the butt, and one at the head.
Drop three balls near one tee, and putt towards the other tee.
Don't stop until you can make three in a row from both 1 and 2 putter lengths.
4 1/2. Stick a short tee into the back of the cup, about 1/2 an inch from the top.
Drop a few balls on the green, and putt the balls so that they hit the tee, then drop in.
It'll teach you to make firm strokes, as well as building confidence. (If you can hit a tee, you can hit a hole)