We study chaotic dynamics and the phase-locking phenomenon of the circular mesh antenna with 1:3 internal resonance subjected to the temperature excitation in this paper. Firstly, the frequencies and modes of the circular mesh antenna are analyzed by the finite element method, it is found that there is an approximate threefold relationship between the first-order and the fourth-order vibrations of the circular mesh antenna. Considering a composite laminated circular cylindrical shell clamped along a generatrix and with the radial pre-stretched membranes at both ends subjected to the temperature excitation, we study the nonlinear dynamic behaviors of the equivalent circular mesh antenna model based on the fourth-order Runge-Kutta algorithm, which are described by the bifurcation diagrams, waveforms, phase plots and Poincaré maps in the state-parameter space. It is found that there appear the Pomeau-Manneville type intermittent chaos. According to the topology evolution of phase trajectories, the phase-locking phenomena are found.