In order to study the relationship between the aging and the polarization/depolarization current (PDC) of transformer oilpaper, a prediction method of transformer oilpaper aging is presented based on the BP neural network with the chicken swarm optimization algorithm. Firstly, the relationship between extended Debye parameters and the polymerization degree (DP) of oilpaper is examined. With the variation of atmosphere temperature, PDC changes and it leads to a failure of extended Debye model to response the aging status of oilpaper. In order to eliminate the error caused by temperature, a BP neural network is trained through fitting PDC and DP of oilpaper. Then, in view of the slow convergence and low efficiency of BP neural network, the chickens swarm algorithm is utilized to optimize weights and threshold of the BP neural network. After the optimization, the network convergence is speeded up and the possibility of trapping into local optimal is also reduced. Finally, the simulation results show that the environment influences to polarization/depolarization current are reduced and the oilpaper polymerization degree is predicted accurately.