Over the last few years; issues regarding the use of hybrid energy storage systems (HESSs) in hybrid electric vehicles have been highlighted by the industry and in academic fields. This paper proposes a fuzzy-logic power management strategy based on Markov random prediction for an active parallel battery-UC HESS. The proposed power management strategy; the inputs for which are the vehicle speed; the current electric power demand and the predicted electric power demand; is used to distribute the electrical power between the battery bank and the UC bank. In this way; the battery bank power is limited to a certain range; and the peak and average charge/discharge power of the battery bank and overall loss incurred by the whole HESS are also reduced. Simulations and scaled-down experimental platforms are constructed to verify the proposed power management strategy. The simulations and experimental results demonstrate the advantages; feasibility and effectiveness of the fuzzy-logic power management strategy based on Markov random prediction.