Most likely a sending unit or bad ground.
For vehicles with an oil pressure gauge, the sending unit (located next to the oil filter) is essentially a variable path to ground for the gauge. When the engine is off, the sender is shorted to ground, and the gauge reads "0" psi (or close), as the oil pressure increases, the sender offers resistance to ground, providing a mid scale readings on the gauge. If the wire is removed altogether, the gauge will read off the scale to the high side (3:00 position) all the time. This is a quick and simple test you can perform to help isolate the problem. With the key ON - engine OFF, pull the wire off the sending unit. The gauge should read full scale. Now short the wire to ground (this will not harm anything), and it should read "0". If this is correct, then your gauge, and the wiring is good, and your trouble is likely to be the sending unit. If this test has little or no effect on the gauge, then your problem is in the wiring or the gauge itself.