In this paper, we will consider the Laplace decomposition method (LDM) for finding series solutions of nonlinear oscillator differential equations. The equations are Laplace transformed and the nonlinear terms are represented by He's polynomials. The solutions are compared with the numerical (fourth-order Runge-Kutta) solution and the solution obtained by the Adomian decomposition method. The suggested algorithm is more efficient and easier to handle as compared to the numerical method. The results illustrate that LDM is an appropriate method in solving the highly nonlinear equations.