Due to the non-Markov property of response of a nonlinear system driven by fractional Gaussian noise（fGn），the diffusion process theory cannot be applied. As an approximate method，the stochastic averaging method for multi-DOF strongly nonlinear systems driven by wideband noise has been applied to study nonlinear systems driven by fGn. The results show that the approximate method is very effective in the response prediction and the reliability analysis. However，so far there has been no analytical analysis on the error and applicability of the approximate method. In the present paper，the approximate method is applied to study a single-DOF nonlinear system driven by fGn and some analytical solutions are obtained. By comparing with reported exact analytical solutions，the error analysis is performed and the applicability of approximate method is determined. The conclusion of the present paper can be the theoretical foundation for further application of the approximate method.