Fuel cell hybrid electric vehicles (FCHEVs) are recognized as a promising solution for vehicle electrification. However, the adoption of FCHEVs is relatively slow due to various factors such as the high cost of hydrogen and the limited lifespan of fuel cells. Therefore, effective energy management strategies are of great interest. Model predictive control (MPC) is widely employed to deal with energy management in FCHEVs. However, conventional MPC often relies on subjective selection of control weights in the objective function and the performance may be compromised. This paper proposes an optimal weight adaptation method within the MPC framework to enhance its effectiveness. The weights in the objective function are dynamically adjusted online using a moving horizon. Optimization techniques are then applied to fine tune these weights. The effectiveness of the proposed MPC controller with adaptive tuning weights is validated under the UDDS drive cycle.