Could be a leaking check valve, but a little more likely it's a problem with the pressure tank.
Turn the pump off, drain the water pressure off, and check the pressure tank with a tire gauge. It should read two psi below your pump cut-on pressure (i.e., if your pump is set for 20-40 cut-on/cut-off, it should be at 18 psi).
If it is low, air it up with a bicycle pump or portable air tank or compressor.
If it won't hold this pressure while not running (the pressure tank should be at the cut-off psi after the pump runs and shuts off), then you probably need to replace the pressure tank. The bladder is shot.
If the pressure tank is O.K., replace the check valve.