The all-wheel drive (AWD) hybrid system is a research focus on high-performance new energy vehicles that can meet the demands of dynamic performance and passing ability. Simultaneous optimization of the power and economy of hybrid vehicles becomes an issue. A unique multi-mode coupling (MMC) AWD hybrid system is presented to realize the distributed and centralized driving of the front and rear axles to achieve vectored distribution and full utilization of the system power between the axles of vehicles. Based on the parameters of the benchmarking model of a hybrid vehicle, the best model-predictive control-based energy management strategy is proposed. First, the drive system model was built after the analysis of the MMC-AWD's drive modes. Next, three fundamental strategies were established to address power distribution adjustment and battery SOC maintenance when the SOC changed, which was followed by the design of a road driving force observer. Then, the energy consumption rate in the average time domain was processed before designing the minimum fuel consumption controller based on the equivalent fuel consumption coefficient. Finally, the advantage of the MMC-AWD was confirmed by comparison with the dynamic performance and economy of the BYD Song PLUS DMI-AWD. The findings indicate that, in comparison to the comparative hybrid system at road adhesion coefficients of 0.8 and 0.6, the MMC-AWD's capacity to accelerate increases by 5.26% and 7.92%, respectively. When the road adhesion coefficient is 0.8, 0.6, and 0.4, the maximum climbing ability increases by 14.22%, 12.88%, and 4.55%, respectively. As a result, the dynamic performance is greatly enhanced, and the fuel savings rate per 100 km of mileage reaches 12.06%, which is also very economical. The proposed control strategies for the new hybrid AWD vehicle can optimize the power and economy simultaneously.