Liquid Hydrogen plays an important role in hydrogen energy society. Therefore it is important to understand its thermal and transport properties accurately. However cryogenic hydrogen has unusual thermodynamic properties because of its quantum nature. The thermal de Broglie wavelength of cryogenic hydrogen molecule becomes the same order as molecular diameter. Therefore, each molecular position and its momentum cannot be defined classically. Because of this nature, hydrogen molecules show higher diffusivity than classical counterpart. Until now, the effects of quantum nature of hydrogen and its mechanism on the thermodynamic properties have not been clarified in detail. Especially, how the quantum nature would effect on the energy transfer in molecular scale has not been clarified. An accurate understanding of the effect and mechanism of quantum nature is important for hydrogen storage method and energy devices which use hydrogen as a fuel. In this study, therefore, we investigated the effect of this quantum nature and its mechanism on the thermodynamic and transport properties of cryogenic hydrogen using classical Molecular Dynamics (MD) method and quantum molecular dynamics method. We applied path integral Centroid Molecular Dynamics (CMD) method for the analysis. First, we have conducted thermodynamic estimation of cryogenic hydrogen using the MD methods. This simulation was performed across a wide density-temperature range. Using these results, equations of state (EOS) were obtained by Kataoka's method, and these were compared with experimental data according to the principle of corresponding states. As a result, it was confirmed that both quantitative and qualitative effect of the quantum nature on the thermodynamic properties of hydrogen are large. It was also found that taking account the quantum nature makes larger virial pressure and weaker intermolecular interaction energy. Second, we have calculated the diffusion coefficient of liquid hydrogen to clarify the effect of the quantum nature on the transport properties. We used Green-Kubo form for the calculation using velocity autocorrelation function. The simulation was performed across a wide temperature range. CMD simulation results were compared with classical simulation results and experimental data. We clarified the effect of quantum nature on the transport properties of liquid hydrogen.