A high-speed motor in a drive system causes several challenges to the reliability of the mechanical parts of electric vehicles and leads to issues with noise, vibration and harshness (NVH). Thus, a two-speed powershift transmission is considered an effective way to improve the dynamic, economic and comfort performance of electric vehicles. A newly designed dual-pump hydraulic control system for a two-speed powershift transmission with two wet clutches is presented, in which the mechanical oil pump is linearly affected by the vehicle speed and the electric oil pump is controllable. By integrating the dynamic model of the hydraulic system into one of the powertrains with a two-speed transmission, a co-simulation dynamic model is proposed. To satisfy the flow and pressure demand of the hydraulic system, a dual-pump control strategy is presented, in which the electric oil pump is controlled by the mechanical oil pump following the minimum energy consumption principle. The World Light Vehicle Test Procedure (WLTP) cycle simulation results show that the energy consumption of the proposed hydraulic system can be reduced by 58.2% compared to the previous single-pump system developed by the authors with a constant main-line pressure control strategy. On the basis, the best configuration of the two pumps can further reduce the energy consumption of the hydraulic system by 23.2% compared to that of two-oil pumps with preset displacement.