Hybrid energy storage system (HESS) is an attractive solution to compensate power balance issues caused by intermittent renewable generations and pulsed power load in DC microgrids. The purpose of HESS is to ensure optimal usage of heterogeneous storage systems with different characteristics. In this context, power allocation for different energy storage units is a major concern. At the same time, the wide integration of power electronic converters in DC microgrids would possibly cause the constant power load instability issue. This paper proposes a composite model predictive control based decentralized dynamic power sharing strategy for HESS. First, a composite model predictive controller (MPC) is proposed for a system with a single ESS and constant power loads (CPLs). It consists of a baseline MPC for optimized transient performance and a sliding mode observer to estimate system disturbances. Then, a coordinated scheme is developed for HESS by using the proposed composite MPC with a virtual resistance droop controller for the battery system and with a virtual capacitance droop controller for the supercapacitor (SC) system. With the proposed scheme, the battery only supplies smooth power at steady state, while the SC compensates all the fast fluctuations. The proposed scheme achieves a decentralized dynamic power sharing and optimized transient performance under large variation of sources and loads. The proposed approach is verified by simulations and experiments.