Hybrid energy storage system (HESS) is an effective solution to address power imbalance problems caused by variability of renewable energy resources and load fluctuations in DC microgrids. The goal of HESS is to efficiently utilize different types of energy storage systems, each with its unique characteristics. Normally, the energy management of HESS relies on centralized control methods, which have limitations in flexibility, scalability, and reliability. This paper proposes an innovative artificial neural network (ANN) based model predictive control (MPC) method, integrated with a decentralized power-sharing strategy for HESS. In the proposed technique, MPC is employed as an expert to provide data to train the ANN. Once the ANN is finely tuned, it is directly utilized to control the DC-DC converters, eliminating the need for the extensive computations typically required by conventional MPC. In the proposed control scheme, virtual resistance droop control for fuel cell (FC) and virtual capacitance droop control for battery are designed in a decentralized manner to achieve power-sharing, enhance lifespan, and ensure HESS stability. As a result, the FC is able to support steady state loads, while the battery handles rapid load variations. Simulation results using Matlab/Simulink demonstrate the effective performance of the proposed controller under different loads and input variations, showcasing improved performance compared to conventional MPC.