Due to the poor dynamic response ability of the fuel cell, the battery is normally applied to integrate with fuel cell to configure the hybrid power system in electric vehicles. In this paper, a vehicle speed prediction model predictive control (SP-MPC) energy management strategy is developed for the hybrid power system in fuel cell electric vehicles. The main principle of the proposed SP-MPC is that the future vehicle total power demand is forecasted via the Markov speed predictor and imported into the energy management system response prediction model to improve the control performance by more accurate disturbance description. The objective function is set for equivalent hydrogen consumption minimization and fuel cell degradation inhibition. As a contrast, the normal MPC strategy, the speed prediction dynamic programming (SP-DP) strategy and the DP offline strategy are formulated. Comparing with the normal MPC strategy, the SP-MPC strategy has a 3.74% reduction in the total operation cost under MANHATTAN condition. The SP-MPC strategy also has a 1.39% reduction in the total operation cost than the SP-DP strategy. Moreover, two scenarios are introduced with different disturbance prediction accuracy to verify the influences of the prediction inaccuracy on the SP-MPC and SP-DP results. For SP-DP strategy, the total operation cost under actual forecast scenario has increased by 5.03% compared with the perfect forecast scenario. The similar result can be seen in the SP-MPC, but the increase between perfect and actual forecast scenario is only 1.02%, which indicates a better robustness to the disturbance prediction inaccuracy compared with the SP-DP strategy. A DSP hardware in loop (HIL) test is conducted for real-time performance verification of the proposed SP-MPC.