The connection of the engine body and the base was simplified as a spring and a damper to analyze the body vibration of the single piston hydraulic free piston engine. It was demonstrated that the increasing of the connection spring rate can reduce the amplitude of the body vibration. But the reduced vibration amplitude was trivial after the spring rate was increased above 300KN/m. The damp ratio of the connection had little influence on the body vibration. The introduction of a pump chamber into the structure in the compression stroke can shorten the rebounding displacement of the free piston assembly (FPA) while it was settled at the right dead center working in pulse pause modulation (PPM) mode. Furthermore it can keep the FPA have an enough stroke to achieve a predetermined compression ratio and reduce the fluctuation of the pump flow. The compression ratio can be improved through increasing the pressure of the compression accumulator and decreasing the pressure of the high pressure accumulator. Also the compression ratio and the operation frequency of the engine can be improved by shortening the switch time of the control valve and prolonging the open time.