In 1935 Einstein, Podolsky, and Rosen (EPR) studied general entangled states in the two photon experiment and pointed out the contradiction between local realism and the completeness of quantum mechanism. Most of the EPR experiments in recent years are based on the detection of polarization correlations of optical photons between spatially separated photon channels, some of which are split and directed to two spatially separated Michelson interferometers. Later, the two arms of Michelson interferometers are replaced by dual-channel Fabry-Perot (F-P) interferometry enabling precise analysis of the energy-time entanglement between a pair of photons. On the other hand, F-P type detectors on gravitational radiation have caught dozens of gravitational wave (GW) events successfully. This paper proposes a combined experiment of EPR and GW, exhibiting whether the coincident rate of EPR is modulated by GW induced change of cavity length or not. Such an experiment could test the coupling of quantum mechanics and general relativity for the first time, and be a useful tool to explore the nature of quantum gravity.