The charging and discharging process of battery energy storage (BES) directly affects its cycle aging. Therefore, considering the cycle aging cost and demand response of BES, this paper proposes a dynamic reconfiguration method of AC/DC hybrid distribution network. By sampling the operation area of charging and discharging power, the BES model in the non-ideal state is reconstructed into a linear model in the convex envelope set of sampling points. On this basis, the cycle aging cost models based on the cumulative throughput and discharge depth are established respectively, and the AC/DC hybrid distribution network reconfiguration model with the minimum comprehensive cost is constructed, and the mixed integer second-order cone programming method is used to solve it. The effectiveness and economy of the proposed reconfiguration method for AC/DC hybrid distribution network are verified by simulation on a modified 33-bus and 70-bus system.