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In this paper, we propose an analytical approach (VIM-Padé) based on the variational iteration method (VIM), Laplace transformation and the Padé approximation. We apply this technique to solve the strongly nonlinear oscillators with cubic and harmonic restoring force. The approximated solutions to the initial value problems are provided and compared with the original variational iteration method solutions and the numerical solutions obtained by Runge-Kutta method. Numerical experiments show that the VIM-Padé technique is efficient for solving the strongly nonlinear oscillators.