This paper is devoted to a kind of stochastic exact controllability of stochastic control system, whose coefficient is time-dependent.The problem is studied from the viewpoint of backward stochastic differential equations, we give a sufficient and necessary condition of stochastic exact controllability for stochastic control systems. If the stochastic system degenerate to deterministic systems, the condition for stochastic exact controllability becomes the counterpart for complete controllability of linear deterministic control systems.