As a key link to ensure the quality of power grid monitoring data,the state estimation provides a reliable data basis for the energy management system. Considering the problems of the large measurement errors and the vulnerability to the cyberattacks in active distribution network,a distributed state estimation method for active distribution network with the false data injection attacks (FDIAs) is studied in this paper. Firstly,the internal state of the subsystem is estimated according to its own measurement,and it is corrected with the global information obtained by the average consensus algorithm,thus the fully-distributed state estimation is realized. Secondly,the weight function is introduced into the subsystem state estimation to modify the weight matrix of the objective extremum function dynamically for improving the robustness of the state estimation. Subsequently,the phasor measurement unit is configured on the boundary nodes and the nodes which are vulnerable to the FDIAs for enhancing the ability to identify the attacks. Finally,the simulations are performed on the IEEE 118-bus distribution network system for verification. The results show that the proposed state estimation method can not only reduce the estimation error effectively,but also identify the FDIAs accurately,which verifies that the accuracy of state estimation and the identification ability of FDIAs are improved.