This paper proposes an optimal energy management approach for a hybrid system of a 5G telecom station. In such systems, it is required to satisfy the energy demand by the load and optimizing the utilization cost and the lifetime of energy storage systems. Furthermore, the battery state of charge should be maintained in some predefined domain to achieve its best performance. A fuzzy logic-based energy management approach is developed to deal with these objectives. The proposed approach satisfies the load demand and optimizes the utilization of the energy storage systems while respecting the limits of the battery state of charge. The performance of the proposed approach is illustrated through simulation results.