Based on the singularity theory, this paper studies the double Hopf bifurcation problem of one rectangular thin plate with simply supported four edges under the combined action of parametric excitation and external excitation in the cases of primary parametric resonance and 1∶3 internal resonance. The bifurcation equation of rectangular thin plate with simple supported edges is obtained by considering the case of weak damping and weak excitation, and the bifurcation diagram of the rectangular thin plate is also given. Taking the damping coefficient, external excitation, excitation parameters and tuning parameters of rectangular thin plate as different values, the equilibrium solutions of thin plate generate Hopf bifurcation, and bifurcate to periodic solutions. The nonlinear vibration form of thin plate system is periodic motion. When the values of other parameters for the rectangular plate satisfy the given conditions, 1∶3 resonant double Hopf bifurcation of the thin plate can be obtained. Subsequently, the four edges-simply supported rectangular plate also show almost periodic vibration.