With coordinated observations of the NOAA 15 satellite and OUL magnetometer station in Finland, we report that the electromagnetic ion cyclotron (EMIC) waves which were stimulated by the compression of the magnetosphere drive relativistic electron precipitation in geoquiescence on 1 Jan 2007. After an enhancement of solar wind dynamic pressure (SWDP), a dayside Pc1 pulsation was observed by the OUL station. Such a Pc1 pulsation is caused by an EMIC wave which propagates from the generation source to lower altitudes. Simultaneously, the NOAA 15 satellite registered an enhancement of precipitating electron count rates with energies >3 MeV within the anisotropic zone of protons. This phenomenon is coincident with the quasi-linear theoretical calculation presented in this paper. Our observations suggest that after a positive impulse of solar wind, the compression-related EMIC waves can drive relativistic electrons precipitation and play a pivotal role in the dynamic of radiation belts.