In this talk, I will introduce an optimal control problem for backward doubly stochastic control system. As a necessary condition of the optimal control we obtain a stochastic maximum principle. We show that the deduced stochastic Hamiltonian system is exactly corresponding to a type of time-symmetric forward-backward stochastic differential equations, which was first introduced by Peng and Shi[C. R. Acad. Sci. Paris, Ser. I, 336 (2003), 773-778]. Applying the stochastic maximum principle to doubly stochastic linear quadratic problems, we obtain the unique optimal control. The existence and uniqueness of solution is proved for a kind of generalized forward-backward doubly stochastic differential equations derived from the maximum principle under some suitable assumptions. The result especially can be used in backward doubly stochastic linear quadratic optimal control problems. An example is given to illustrate the theoretical results. This talk is based on the work jointly with professor Peng Shige and professor Wu Zhen.