We present a quadrature phase-shift keying (QPSK) signal demodulator that combines the graphene photodetector with symmetrical electrodes and an optical hybrid based on standing wave interference to demodulate the QPSK signal. Compared with a conventional QPSK demodulator, which contains a hybrid based on multimode interference couplers and two pairs of balanced detectors, the proposed demodulator can greatly decrease the complexity and size. The simulation with the finite-difference time-domain method demonstrates that the demodulator can achieve QPSK signal extraction. We further discuss the effective responsivity, bandwidth, and error vector magnitude of the QPSK constellation diagram. The scheme will provide a feasible approach for realizing high-speed compact QPSK coherent receivers theoretically.