Due to the complexity and timeliness of the dual power source control system for range extended electric vehicles, a real-time predictive fuzzy energy management strategy based on speed prediction, which comprehensively takes into account the demand power of auxiliary power unit, future average speed and driving distance is proposed in this work. Firstly, to improve the topicality and accuracy of the control system, the convolutional neural network with long short-term memory neural network (CNN-LSTM) algorithm is adopted to predict the future driving speed by the speed features and adjacent speeds. Secondly, taking account of the characteristics of the driving conditions for electric logistics vehicles, a three-inputs-one-output fuzzy controller is formulated based on the average predicted speeds, current traveling distance and demand power of the auxiliary power unit, so as to adjust the expected output power to harmonize the fuel consumption, electricity costs for the process of battery charging, discharging and degradation. Besides, the comparative tests are carried out to validate the effectiveness of various control strategies for harmonizing fuel consumption and battery degradation. The results under the World Light-duty Vehicle Test Cycle (WLTC) indicate that compared with the fuzzy control strategy which only takes the current vehicle speed as an input variable and the charge-depleting charge-sustaining (CD/CS) strategy, the total operation cost of the proposed strategy is reduced by 3.04% and 34.44%, respectively. Finally, The robustness and effectiveness of the strategy are verified under various driving conditions, and the real-time performance of the strategy is verified by HIL experiment. Hence, the proposed real-time predictive fuzzy energy management strategy gives out the great control effect on economy improvement and suppression of battery decay for electric extended-range vehicles.