The internal resonance of strongly non-linear autonomous systems with multi-degrees of freedom was analyzed on the basis of modifying the KBM method, and the amplitude of limit cycles and the approximate solution were obtained. Compared with KBM method, the characteristic of the present method was that the term included in the approximate solution was a nonlinear function of time instead of a linear function, which could increase the accuracy and be used extensively. An example was given, whose approximate solution and phase-space trajectories were obtained. The results computed by this method were in pretty good agreement with the numerical results, and the accuracy of the present method was very good.