A general maximum principle for optimal control problems derived by forward-backward stochastic systems is established, where control domains are non-convex and forward diffusion coefficients explicitly depend on control variables. These optimal control problems have broad applications in mathematical finance and economics such as the recursive mean-variance portfolio choice problems. The maximum principle is applied to study a forward-backward linear-quadratic optimal control problem with a non-convex control domain; an optimal solution is obtained. (C) 2013 Elsevier Ltd. All rights reserved.