A refined asymptotic perturbation method was proposed and used to investigate the nonlinear dynamical behavior of twodegreeoffreedom systems with quadratic and cubic nonlinear terms under one-to-three internal resonance. Based on the averaged equations and the original differential equations, the frequency response curves and bifurcation diagrams were obtained respectively. Different from the original asymptotic perturbation method, the effectiveness of the refined asymptotic perturbation method for one-to-three internal resonance cases was shown.