Based on the emerging low-cost, non-contact current sensors, a topology identification method based on multi-period mixed integer linear optimization was proposed in this paper. Firstly, a mixed integer nonlinear optimization (MINLP) model for topology identification was established based on the absolute value error of branch current. Then, the MINLP model was transformed into a mixed integer linear optimization (MILP) model by linearization method, and a multi-period optimization model was established through multi-period measurement data, so as to eliminate the influence of pseudo measurement error. In addition, the optimal configuration condition of branch current sensors was proved to ensure the accuracy of topology identification. The simulation results of IEEE-33 node system show that the proposed method in this paper has the high accuracy of topology identification. With the increase of multi-period scenarios, the accuracy of topology identification gradually increases, and the influence of pseudo measurement error is greater than that of branch current measurement error.