Based on the theory of layered displacement field and the geometric nonlinearity of von Karman's large deformation, a nonlinear motion partial differential equation of composite material lattice truss sandwich panels was established using the Hamiltonian principle. Then, the vibration partial differential equation of the sandwich panels was discretized into ordinary differential equations using the Galerkin method. Finally, a multi-scale method was used to solve and obtain the nonlinear modulation equation of the composite lattice sandwich panel under the conditions of 3:1 superharmonic resonance and 1:3 coexisting internal resonance. Through numerical calculations, the amplitude value of the composite lattice sandwich panel shows a decreasing trend with the increase of external excitation amplitude during superharmonic resonance. The indirectly excited second mode is sensitive to the response of different micro cell configuration changes, while the first mode is essentially not affected by the cell configuration.