As an initial step to develop a liquid hydrogen pump of piston type operated under cryogenic and high pressure, leakage and piston head shape for the piston pump were discussed with temperature and pressure. As the results, the leakage depended on correlation among density, viscosity, clearance area by the low temperature. In order to reduce the leakage, it was found that the air-tightness can be improved by minimizing contact surface between piston and cylinder, and also increasing pressure in-cylinder can reduce piston clearance. Among the proposed piston shapes, D type piston shape had the most air-tightness. D type piston had smaller contact surface than other piston shape and easier expansion of cup shape by pressure. The leakage of D type piston shape was found about 7%, compared with A type piston shape. But it was required that analyze about vapor lock by friction and wear resistance.