In order to complete the reasonable parameter matching of the pure electric vehicle (PEV) with a hybrid energy storage system (HESS) consisting of a battery pack and an ultra-capacitor pack, the impact of the selection of the economic index and the control strategy on the parameters matching cannot be ignored. This paper applies a more comprehensive total cost of ownership (TCO) of HESS as the optimal target and proposes an optimal methodology integrating parameters and control strategy for the PEV with HESS. Through the integrated optimal methodology, the application value of HESS is analyzed under various types of driving cycles and the results indicate that the HESS can significantly improve the economic performance of PEVs under both urban and suburban driving cycles. Due to the poor adaptability of traditional control strategies to different driving cycles, a novel extreme learning machine (ELM) based controller is established. Firstly, a dynamic programming (DP) based controller is applied for the offline optimization of the HESS power allocation under several typical driving cycles. Then, an analytical method combining correlation analysis and mean impact value (MIV) is employed to deal with offline sample data from DP and obtain the characteristic variables of the ELM model. Ultimately, the instantaneous power allocation strategy of HESS is acquired by utilizing ELM to learn offline data of HESS. Comparative simulations between the ELM-based controller and the rule-based controller are conducted, and the simulation results show that compared to the rule-based controller (RBC), the ELM-based controller reduces the electricity consumption by 3.78% and battery life loss by 6.51%.