Given the complexity of the dielectric relaxation response of transformer oil-paper insulation, this paper establishes a hybrid equivalent circuit new model to characterize the relaxation process of an oil-paper insulation system according to the characteristics of the oil-paper insulation and Maxwell circuit theory. The theory of a hybrid equivalent circuit offers a solution for the hybrid equivalent circuit parameters and the recovery voltage. On the basis of the hybrid equivalent circuit, it puts forward a new method to diagnose the aging condition of transformer oil-paper insulation by using the p parameter to lay the foundation for the follow-up insulation diagnosis. The results show that: the p parameter of the hybrid equivalent circuit has nothing to do with the polarization voltage and the charging time, and it can accurately diagnose the aging condition of the transformer oil-paper insulation system by using the function expression between the water content of the transformer oil-paper insulation system and the p parameter, when p is in the interval (+∞, 0.323), the transformer is well-insulated. When p is in the interval (0.193, 0.323), the insulation of the transformer is in a relatively serious condition, the value of p in the interval (0, 0.193) indicates serious aging insulation in the transformer. This work is supported by National Natural Science Foundation of China (No. 51407151).