A few MHD simulations have been performed to study the interaction between a propagating interplanetary shock and Earth's standing bow shock, followed by the magnetosheath and magnetopause. They satisfactorily explain the deceleration of the interplanetary shock in the magnetosheath, which was observed a few dozen times by well-arranged satellites. In this work, we perform a hybrid particle-in-cell simulation in a similar setting with a self-consistently developed quasi-perpendicular interplanetary shock. We track the position of the interplanetary shock as it travels through the magnetosheath. We show that early in the propagation through the magnetosheath, the interplanetary shock slows down, which is in line with the conclusion of previous studies. Later in the propagation, however, we find that -- in the plane perpendicular to the interplanetary magnetic field -- the interplanetary shock travels faster inside the magnetosheath than it does in the solar wind. We also note that as the magnetic field lines are stretched along the magnetopause, the interplanetary shock becomes quasi-parallel close to the magnetopause.