In this article, we give an analytical approximate solution for non-linear quadratic optimal control problems using the variational iteration method (VIM). First by means of the Pontryaginâ maximum principle the non-linear two-point boundary-value problem (TPBVP), transformed into an initia value problem (IVP), then we construct variational iteration correction functional to find the approximate solution. Finally, an example is given to illustrate the efficiency and applicability of the proposed method.