An interplanetary (IP) shock has a large impact on magnetospheric ions. Satellite observations have shown that soon after arrival of the IP shock, overall intensity of the ions rapidly increases and multiple energy dispersion appears in an energy‐time spectrogram of the ions. In order to understand the response of the magnetospheric ions to IP shock, we have performed test particle simulation under the electric and magnetic fields provided by the global magnetohydrodynamic simulation. We reconstructed the differential flux of H+, He+, and O+ ions at (7, 0, 0) Re in GSM coordinates by means of the semi‐Lagrangian (phase space mapping) method. Simulation results show that the ions respond to the IP shock in two different ways. First, overall intensity of the flux gradually increases at all pitch angles. As the compressional wave propagates tailward, the magnetic field increases, which accelerates the ions due to the gyrobetatron. Second, multiple energy‐time dispersion appears in the reconstructed spectrograms of the ion flux. The energy‐time dispersion is caused by the ion moving toward mirror point together with tailward propagating compressional wave at off‐equator. The ions are primarily accelerated by the drift betatron under the strong electric field looking dawnward. The dispersion is absent in the spectrogram of equatorially mirroring ions. The dispersion appears at higher energy for heavier ions. These features are consistent with the satellite observations. Because the acceleration depends on bounce phase, the bounce‐averaged approximation is probably invalid for the ions during the interval of geomagnetic sudden commencement. Plain Language Summary Solar storm can cause a significant compression of the magnetosphere on the dayside. The compression starts at the subsolar point and propagates toward the nightside in the magnetosphere. Some ions bouncing between the Northern Hemisphere and the Southern Hemisphere are found to be accelerated selectively when the ions move together with the propagation of the compressional wave. As a consequence, striped structures appear in the energy versus time spectrum of the ion. Key Points Magnetospheric ions respond to IP shock in different ways; rapid increase in flux at all pitch angles and multiple energy‐time dispersion Energy‐time dispersion is caused by ions moving toward the mirror point together with tailward propagating fast mode wave Energy‐time dispersion appears at higher energies in spectrograms of heavier ions. The dispersion is absent in equatorially mirroring ions.