It is important to identify the critical transmission node of a power gird accurately and comprehensively. Given that the current method does not consider the power transmission path distribution between nodes and the transmission characteristics of different type nodes, then based on complex network theory and a PageRank algorithm, a directed weighted network model of a power grid is established from the perspective of static analysis. From the characteristics of nodes in the power transmission path, the nodes are divided into power, intermediate and terminal nodes. The information value and unequal probability transmission characteristics between different type nodes and adjacent nodes are considered, and an electrical transfer matrix is obtained by considering node state information and topology information based on the improved PageRank algorithm. The critical node identification method is established by the node voltage, node degree and node transfer characteristics. From the comparison and analysis of simulation results, and combining with the changes of network transmission efficiency after the system is subjected to a static deliberate attack, it is shown that the identified critical nodes have a great impact on the transmission capacity of the power grid, and the correctness and superiority of the identification method are verified. This work is supported by the National Natural Science Foundation of China (No. 51877174).