In order to solve the problem of numerical oscillation in electromagnetic transient numerical calculation, a 3-step 4-order implicit Taylor series method with infinite stability is applied to the numerical calculation of electromagnetic transient. Compared with the implicit trapezoidal integration method, the numerical integration method is both A-stability and infinite stability. And it has 6 order calculation accuracy. Thus, the method has a fast decay rate for the truncation error, which can effectively suppress the numerical oscillation. The numerical results show that the proposed method can be free of numerical oscillation effectively when sudden change happens. Besides, compared with the critical damping method, using the proposed method to implement electromagnetic transient calculation can take a larger time integration step, which can get higher computational efficiency. This work is supported by National Natural Science Foundation of China (No. 51407104).