Based on some theories,and to analyze transformers and many different models to compare, a new kind of transient mathematical model on transformers is presented. In the model, the saturation of magnetic circuit and core losses are considered and the effects of nonlinearity of main magnetic circuit for voltage and current of transformers are analyzed. Then the applications range and the direction to improve of the model are referred to through comparing the model with other models. And the feasibility and accuracy of the model are verified through comparing the results of simulation with the results of experiments.