Topology error identification is the premise of network topology analysis, and network topology analysis is the basis for implementing various advanced applications of Distribution Management System (DMS). In the distribution network, due to insufficient collection of telesignalization information and poor real-time performance, the switch state is prone to errors or even unknown, which leads to a high proportion of multiple topology error. Therefore, a method of identifying distribution network topology error based on D-PMU and branch state function is proposed in this paper, which comprehensively uses telemetry and telesignalization information to identify single topology error and multiple topology error in the distribution network. On the basis of the Weighted Least Squares (WLS) State Estimation, the variables that characterize the on/off state of the branch are augmented into the state variables. The influence of branch state variable on node admittance matrix is analyzed to obtain the augmented Jacobian matrix. At the same time, the corresponding branch state function is constructed to realize the transformation of branch state variable from discretization to continuity. The case studies of single and multiple topology error are set in the IEEE-33 system, where some nodes are equipped with D-PMU units. The result shows that the proposed method can realize the identification of distribution network topology error.