The periodic motion of a simplysupported rectangular honeycomb sandwich plate under the combination of the parametric and transverse excitations is investigated by the improved fourdimensional subharmonic Melnikov method. Based on periodic transformations and Poincaré map, a fourdimensional subharmonic Melnikov function is obtained. Then, a main theorem, which can be used to determine the existence of the periodic orbits for the fourdimensional nonautonomous nonlinear dynamical system, is presented. The periodic motion of the honeycomb sandwich plate under 1∶2 internal resonance is then studied by the improved method. The certain parameter regions where the periodtwo motion may occur are obtained. Numerical simulations are also carried out to verify the analytical predictions.