For solving the transient current measurement problem in the process of Power system running, this paper used the Boundary Element Method to research, and analyzed the method of solving the eddy current field non-source area scalar magnetic potential by the boundary element method with surface impedance concept: to measure the magnetic field of a particular point by the Magnetic Sensor Array, and to solve the inverse problem of reconstructing transient current by the same idea, the model building process of the algorithm was proposed, and the simulation's results showed the efficiency.