In this paper, a new and innovative semi-analytical method called Akbari-Ganji’s method (AGM) has been applied to solve nonlinear equations of the semicircular oscillator. The major concern is to achieve an accurate solution that has an efficient approximation according to the Runge-Kutta numerical method. The results are presented for different values of parameters to demonstrate the applicability of this method. It was found that the proposed solution is very accurate and efficient for the discussed problem. It is worthwhile to mention that not only do convergence problems for solving nonlinear equations by using AGM appear small, but the results also demonstrate that the AGM could be applied to nonlinear problems with high nonlinearity.