In this paper, a piezoelectrically driven single piston pump is designed for high delivery pressure and large displacement. It is composed of a piezoelectric stack, a hydrostatic amplifier and a plunger with two check valves from a radial plunger pump commercially available. Passive check valves instead of active membranes in the pump allow higher pressure delivery, and the hydrostatic amplifier is adopted for larger displacement of the pump. In order to study delivery characteristic of a piezoelectrically driven single piston pump, numerical simulation of unsteady flow inside the pump is conducted by computational fluid dynamics (CFD). Moving mesh technique is adopted to characterize the behavior of two check valves for oil distributing. Influences of typical design and operation parameters on delivery performance of the single piston piezo pump are analyzed. The results show that, driving frequency and spring stiffness of the valves and chamber configuration should be properly designed for stable oil delivery with low flow ripple as possible. Numerical simulation is valid to describe the behavior of the pump, on target for theoretical reference to its counterparts used in miniature EHA actuators.