The distributed economic dispatch model has advantages of better robustness, faster computation and less communication, and is suitable for active distribution networks with a high penetration of distributed power sources. However, the time delay in communication between units in the distributed model will likely undermine the stability of the system. So in this paper the time delay stability of active distribution networks adopting a distributed economic dispatching strategy is studied. First, a fully distributed economic dispatch strategy is designed by introducing virtual distributed power sources. Then a stability analysis model under symmetric and asymmetric time delay of active distribution networks using this strategy is established. The Lyapunov stability theorem and the free power matrix method are also used to derive a lower conservative criterion for the time delay stability of the system, and the stability margin of the time delay system is calculated by means of linear matrix inequalities. Finally, the correctness and validity of the delay stability analysis and delay stability margin calculation methods of the system are verified by simulation examples in the IEEE-14 node distribution network. This work is supported by the National Natural Science Foundation of China (No. 52107122).