Aiming at the problems of AC/DC hybrid distribution network node voltage instability, high rate of abandoned wind and photovoltaic power and high system operation and maintenance cost caused by source-load volatility, a low-carbon optimization operation method of AC/DC hybrid distribution network taking into account network reconfiguration and demand response is proposed. Firstly, a stepped carbon trading model for AC/DC hybrid distribution networks is established. Secondly, a low-carbon optimization operation model for AC/DC hybrid distribution networks is developed with the optimization objectives of system economy and low-carbon, taking into account the constraints of network reconfiguration, demand response, capacitor switching, access to distributed power sources, and charging/discharging of energy storage. Then, the nonconvex distribution network optimization model is transformed into a mixed-integer convex planning model and solved by introducing intermediate variables and a second-order cone relaxation method. Finally, the proposed method is simulated and analyzed by the improved IEEE 33-node AC/DC hybrid distribution system, and the results show that the proposed method can significantly reduce the carbon emissions and the rate of wind and photovoltaic power abandonment generated by the system operation, and improve the system voltage stability and dispatch economy.