Hybrid electric vehicles (HEVs) are used as a bridge during the transition to battery electric vehicles (BEVs) and to make energy consumption more efficient. The main problem in improving the efficiency of HEV energy consumption is torque management. In this study, a novel approach based on a nonlinear model predictive controller to solve the reference tracking and torque distribution problem is proposed. That is to say, in order to increase the efficiency of torque distribution, the weights of nonlinear model predictive control (NMPC) are trained with a Deep Q Network (DQN), and an event-triggered mechanism is designed with DQN to reduce the computational cost of MPC. The considered torque distribution problem varies according to the type and structure of the HEV. In this study, a parallel type 2 hybrid electric vehicle (P2 HEV) is considered and modeled via publicly shared passenger vehicle data of the engine, motor, high-voltage battery, transmission, clutch, differential, and wheel characteristics. NMPC is formulated so that the torque values remain within the physical limits of the engine, and the battery also operates at its physical limits. Namely, it is guaranteed that the battery works according to a certain state of charge (SOC) window and current limits. The state of health (SOH) of the battery is also considered in the optimization. The motor and engine efficiencies increase by 3.61% and 2.86%, respectively, with the proposed control structure, while the computational cost is reduced by 52.01% when utilizing the proposed event-triggering mechanism in the NMPC controller.