The entry of solar energetic protons in the energy range from 100 keV to 10 MeV into the Earth's magnetosphere is simulated to examine the effect of shock drift acceleration at the quasi-perpendicular bow shock. The proton trajectories are traced from the upstream side of the solar wind in time-dependent electric and magnetic fields obtained from global MHD simulation data. To investigate the efficiency of the shock drift acceleration, the dynamic pressure (density) of the solar wind is increased. We find that when the dynamic pressure is increased, the proton flux entering the magnetosphere is increased and the cutoff latitude becomes lower. We show that protons having energies on the orders of 100 keV and 1 MeV and reaching the inner magnetosphere can experience shock drift acceleration at the quasi-perpendicular bow shock when the dynamic pressure is increased. We further show that the shock drift acceleration of solar protons up to energies on the order of 1 MeV is possible at the Earth's bow shock, which is consistent with the observation.