Extended-range electric vehicles are considered to be the most promising pure electric vehicles that can achieve lower fuel consumption and emissions. However, during vehicle operation, range extenders cause an increase in noise, vibration and sound vibration harshness (Noise, Vibration, Harshness, NVH) during startup and operation, which can significantly reduce passenger comfort. Therefore, this study proposes a multi-objective predictive energy management strategy (MPC-NVH-Rapid DP) that can find a balance between the range extender fuel consumption, power cost, and range extender NVH. First, the multi-objective energy management problem is formulated as a total operating cost minimization problem, and an optimization strategy for range extender point selection considering NVH is designed. Subsequently, the accuracies of Long Short-Term Memory (LSTM), Bidirectional LSTM (Bi-LSTM) and Convolutional Neural Network-LSTM (CNN-LSTM) for speed prediction in model predictive control (MPC) are compared, and a multi-objective algorithm based on MPC and NVH considerations is proposed as an energy management optimizer. Finally, the real-time performance of the proposed MPC-NVH-Rapid DP strategy is verified by MATLAB/Simulink and hardware-in-the-loop tests, and the results show that the proposed strategy achieves better NVH performance and improves driving comfort at the expense of partial fuel economy.