The model of nonlinear disturbed mechanism for one-dimensional Fermi gas is investigated. Firstly, the corresponding functional is constructed; secondly, its Lagrange operator is selected; using the modified generalized variational iteration method, the approximate analytic solutions of corresponding path curves are obtained. A simple example is given, and the approximation accuracy obtained by using the modified generalized variational iteration method is shown to be better. The aim of this article is to provide a valid method of solving the nonlinear physical problems.