We develop an importance sampling simulation scheme for estimating extremely small probability of level exceedance with respect to a nonlinear oscillating systems driven by a stationary random noise, where we use a probability measure transformation technique for constructing a simulation scheme based upon the Maruyama-Girsanov theorem. First, a system of Itô random differential equations and the related level exceedance are formulated, where the system nonlinearity is incorporated in terms of a nonlinear restoring force based upon the Masing rule. Next, an importance sampling simulation scheme is constructed, in which the optimal selection of the importance sampling measure is newly proposed. Finally, we give some numerical examples to demonstrate the efficiency of the proposed scheme and quantitatively examine effects of model parameters as well as the nonlinearity.