Considering the problem of out-of-stock and inventory overstock caused by dual-channel supply chain inventory system, three dynamic optimization models of three modes: single control, centralized control and cross-replenishment control of dual-channel inventory were established under the condition that both online and offline channels are facing stochastic demand. Firstly, based on the dynamic differential equation of inventory, guided by the control theory creatively, and by means of Taylor expansion and Laplace transformation, the feedback transfer function of dual-channel inventory system was obtained. Secondly, considering the periodic interactions, upstream and downstream interactions and inter-channel interactions in the process of cross-replenishment’s purchase-sale-stock, delay control, feedback control and Proportion-Integral-Derivative (PID) control were used to construct a complex interactive system with two inputs and two outputs, so as to explore the dynamic balance between supply and demand of the dual-channel inventory system itself and among channels, optimize the dual-channel inventory holdings, reduce the out-of-stock times and amount and keep them to a dynamic equilibrium. Finally, through numerical simulation experiments, three dual-channel inventory control strategies were compared. The simulation results show that when on online and offline channels were facing different distributions of stochastic demand, the residual stock of cross-replenishment control decreased by 4.9% compared with that of single control, and the out-of-stock rate of cross-replenishment control decreased by 66.7% and 60% respectively compared those of single control and centralized control. The experimental results show that when online and offline channels are facing different distributions of stochastic demand, the use of cross-replenishment strategy can effectively reduce inventory holdings, reduce the times and amount of out-of-stock, and thus save the inventory costs.