The effects of ion motion on the generation of short-cycle relativistic laser pulses during radiation pressure acceleration are investigated by analytical modeling and particle-in-cell simulations. Studies show that the rear part of the transmitted pulse modulated by ion motion is sharper compared with the case of the electron shutter only. In this study, the ions further modulate the short-cycle pulses transmitted. A 3.9 fs laser pulse with an intensity of 1.33×1021 W cm-2 is generated by properly controlling the motions of the electron and ion in the simulations. The short-cycle laser pulse source proposed can be applied in the generation of single attosecond pulses and electron acceleration in a small bubble regime.