Abstract: Extreme disasters can cause varying degrees of damage to the distribution and transmission networks, affecting the normal operation of the power system. After a failure occurs, a reasonable recovery strategy is beneficial for rapidly restoring power supply and reducing outage losses. Aimed at the scenarios where extreme disasters cause simultaneous multiple failures in distribution and transmission networks, this paper proposes a collaborative post-disaster recovery strategy for distribution and transmission networks based on multi-period Anderson acceleration, which coordinates the resources of both networks. The strategy targets minimizing operation costs during the recovery process, considers the operating status of generating units in the transmission network and the fault repair sequence, and also incorporates the flexible resource response of the distribution network, the fault repair sequence, network reconfiguration, and islanding strategies. A fully parallel analytical target cascading method is adopted to solve the model. To address the issue of poor convergence in the inner loop of the analytical target cascading method caused by the changes in network topology, an extended multi-period Anderson acceleration method is applied in the solving process. The T30D2 and T57D8 test cases demonstrate that the proposed method can effectively reduce the power outage losses during the post-disaster recovery process and significantly improve computation speed, showing good adaptability for the large-scale network with the integration of multiple active distribution networks.