The distribution network is connected to new elements such as distributed new energy and controllable resources, and the traditional state estimation model is faced with new problems such as incomplete measurement information, frequent topology changes of the distribution network and load time series fluctuations, which lead to reduced accuracy of the model estimation. Therefore, a method of distribution network state estimation by fusing improved generative adversarial network and graph attention network is proposed in this paper. Firstly, topological parameters and measurement information in different historical time sections are selected to generate data sets. The incomplete measurement information is filled by introducing the bidirectional long short-term memory (BiLSTM) network into the generative adversarial network. Secondly, the graph attention network is used to capture the spatial dynamic relationship between the nodes adaptively, and the bidirectional long short-term memory network is used to fully excavate the time-coupling relationship of the cross-sectional sequence information in different time sections. These networks are concatenated to form the spatiotemporal feature expression of the measurement to the state, and the state estimation model of the improved graph neural network is obtained. Finally, simulation experiments are carried out in IEEE 118-bus system, and compared with other neural network algorithms such as convolutional neural network and graph attention network. The results show that the proposed algorithm has better performance in the case of missing data and time-varying topology than other neural network algorithms.