Composite laminated materials are better capable of mechanical and thermal characteristics, which have been used in a wide variety of large-scale modern structures. In this paper, the existence and bifurcation of periodic solutions for a three degree-of-freedom symmetric cross-ply composite laminated rectangular thin plate with 1:3:3 internal resonance are investigated in detail. Firstly, we perform scale transformations for variables to get the nonlinear averaged equations for the symmetric composite laminated rectangular thin plate. Secondly, the Melnikov function is obtained by establishing curvilinear coordinate frames and constructing Poincaré maps, which can be used to discuss the upper bound of the number of the periodic solutions. Finally, the phase portraits are given to show the number and corresponding positions of periodic orbits for the composite laminated plate. The results we obtained can provide great theoretical support for the stability analysis of symmetric cross-ply composite laminated rectangular thin plate.