In this paper, a power management strategy for a photovoltaic (PV)/battery system in an islanded DC microgrid is proposed based on a Model Predictive Control (MPC) approach. A PV system and a battery storage source are connected to a common DC bus through two DC/DC converters that are providing power to the loads. The considered PV-Battery system is presented by a nonlinear model with four operational modes. As part of the proposed MPC power management strategy, an optimization problem is formulated to meet the voltage performance in the system with respect to operating conditions and constraints. The aim of the proposed MPC is to control the DC/DC converter to extract the maximum power from the PV system under different weather conditions and also to control the bi-directional DC/DC converter for charging and discharging the battery by considering the State of Charge SoC of the battery. The battery storage source is incorporated into the system to compensate power generation due to possible fluctuation in PV or changes in load demand, and as a result, to regulate DC bus voltage and supply the loads when necessary. The simulation results demonstrate the validity of the proposed method.