A subsurface hydraulic pump using high pressure accumulator, which comprises a subsurface hydraulic reciprocating pump, comprising a large diameter cylinder and piston and a small diameter cylinder and piston. The cylinders are attached to each other at their open ends and the pistons are attached to each other with a single piston rod. The small cylinder is connected to the well tubing, from which the pump system is hung at the bottom of a well, with the complete pumping system emersed in well liquids. Two check valves are provided in the small cylinder, one for the entry of well fluids on the down stroke of the small piston and a second one which permits flow upwardly from the small cylinder into the tubing, on the upstroke of the small piston. A continuously driven hydraulic pump and a valve system are provided such that in one position of the valve the hydraulic pump withdraws liquid from the large cylinder and pumps it into a high-pressure accumulator, and on the reverse position of the valve, the pump accepts the high pressure liquid from the accumulator and pumps it at additional pressure into the large cylinder, forcing the large piston and small piston upwardly, lifting fluid into the tubing and up to the surface.