Based on the nonlinear governing equation of the carbon nanotubereinforced composite plate, the averaged equation under 1〖DK〗∶3 internal resonances is obtained by using the method of multiple scales. It is then simplified by means of the normal form theory. The nonlinear dynamics of the unperturbed system and the effect of the perturbation terms on the manifold are investigated. Energyphase method is used to validate the existence of the multipulse jumping orbits. It is eventually to approved that chaotic dynamics in the sense of Smale horseshoes takes place at the carbon nanotubereinforced composite plate under certain parameters. The results also provides essential data for theoretical analysis and engineering practice.