The previous state-of-charge (SOC) and state-of-health (SOH) management strategies for battery energy storage system based on the modular multilevel converter (MMC-BESS) normally work separately. With the diversification and complexity of energy storage application scenarios in AC/DC hybrid grid, it is necessary to develop more flexible battery management strategies for different scenarios. In this paper, a multidimensional battery management strategy is developed, which takes into account both SOC and SOH, and also considers both intra-submodule (intra-SM) equalizing and inter-SM balancing. Experiments are presented to verify the proposed strategy for MMC-BESS.