Josephson mixer is a kind of circuit which can generate entangled quantum microwave signals. An equivalent circuit model of Josephson mixer is established. Quantization is carried out on three-wave mixing Hamiltonian. Influences of the critical current of Josephson junction, shunt linear inductance, equivalent inductance of resonator transmission line and applied effect of flux through the ring on three-wave mixing intensity are investigated. Simulation results show that the critical current of Josephson junction determines the maximum value of the chosen linear inductance, but has little influence on three-wave mixing intensity. The value of linear inductor determines the optimal value of flux through the ring and maximum value of three-wave mixing intensity. Resonator transmission line equivalent inductance is the smaller the better in the allowable range. It is of great value to choose circuit component parameters effectively and improve the generating ability of entangled quantum microwave.