Microgrid systems are becoming a very promising solution to meet the power demand growth especially in remote areas where diesel generators (DG) are commonly used as a main energy source. Photovoltaic (PV) systems are commonly used as a sustainable energy source to economize DG fuel. Due to the intermittent and fluctuating behavior of PV generators, energy storage systems (ESS) such as electrochemical battery are suggested. PV and ESS are usually connected using one inverter/charger called hybrid inverter. The power management is crucial to optimize the fuel consumption and operate efficiently ESS. Additionally, in an off-grid operation, the microgrid frequency becomes sensible due to the slow dynamic of DG which requires an additional control tool to improve the frequency regulation. This paper proposes a new power management based on Mamdani fuzzy logic. The proposed controller considers the targets mentioned above by only controlling the hybrid inverter. Simulation results prove that fuzzy-based controller reduces the DG fuel consumption by more than 12% compared to classical hysteresis management control. Moreover, the proposed controller performs efficiently regarding the conventional frequency regulation, which is widely used in microgrid control.