A new homotopy technique based on the parameter expansion (PEHAM) was proposed to strongly nonlinear oscillation. By means of the technique of parameter expansion and the theory of homotopy, we transformed the original nonlinear dynamical system into a set of linear differential equations which can be solved easily. This method is a more general one in which the magnitude of the nonlinear need not be a small parameter. A typical cubic system in the form of oscillator was employed to show its feature. Not only the zeroth and firstth approximation of the conservative Duffing oscillator but also the approximate period were obtained by the method. The results verify that when αis not a small parameter, even when α→∞,the relative error between the exact period and the approximate period exceeds no more than 3% . The analytical results obtained by the method agreed well with the numerical result obtained by the forth order RungeKutta method.