There is a problem of how to coordinate the operation strategy of coupled transmission and distribution networks to achieve a win-win situation in the market environment. Thus a cooperative economic dispatch strategy of coupled transmission and distribution networks based on the Stackelberg game is proposed. First, a bi-level optimization model is established to solve the economic dispatch of coupled transmission and distribution networks using Stackelberg game architecture, in which the upper level is the transmission network price clearing model and the lower level is the economic dispatch model of each distribution network. This considers second order cone alternating current power flow constraints. Then, the second order cone reconstruction technique, KKT (Karush-Kuhn-Tucker) conditions, strong duality theorem and linear relaxation technique are applied to transform the proposed bi-level model into a mixed integer second-order cone programming single-layer model for analysis. Finally, the simulations verify the effectiveness of the proposed model and method. The results show that the proposed cooperative economic dispatch strategy can effectively reduce the clearing price of transmission energy and reserve, and reduce the operational cost of the distribution networks. This work is supported by the Science and Technology Project of Jilin Province (No. 20210508031RQ).