You have a short.

Either the power wire between the fuse and the pump motor is worn through,
or a winding in the motor itself is shorted. The motor could be drawing a
heavy load which requires more current than the fuse can accomodate. Given
these choices, my money is on the pump needing to be replaced.

To test the wire, remove the fuse and unplug the motor, then test with a
multimeter to see if there is continuity to ground. The answer should be no
continuity.

There ought to be no other load on the fuel pump circuit, but if you bought
the car used, this might not be true any longer, and the auxiliary circuit
might be causing the problem.