In this study we have investigated the determination of proper time step in molecular dynamics simulation.Since the molecular dynamics is mathematically related to nonlinear dynamics, the analysis of eigenvalues isused to explain the relationship between the time step and dynamics. The tracings of H2 and CO2 molecular dynamics simulation agrees very well with the analytical solutions. For H2, the time step less than 1.823 fs pro-vides stable dynamics. ForCO2, 3.808 fs might be the maximum time step for proper molecular dynamics. Al-though this results were derived for most simple cases of hydrogen and carbon dioxide, we could quantitatively explain why improperly large time step destroyed the molecular dynamics. From this study we could set the guide line of the proper time step for stable dynamics simulation in molecular modeling software.