A new adaptive delay-dependent fault-tolerant shape control strategy is proposed for the stochastic distribution system with time-delay, which can effectively make the output probability density function (PDF) track a given target distribution. In this framework, firstly, a system model based on PDF with the actuator failure is constructed. And then, an adaptive delay-dependent fault-tolerant controller, which include a normal controller and an adaptive compensation controller is designed. The normal controller can track the given output distribution with an optimized performance index when there is no actuator fault, and the adaptive compensation controller can reduce the negative effects caused by the actuator fault. Numerical simulations are used to show the effectiveness of the proposed method.