Standalone microgrids with photovoltaic (PV) solutions could be a promising solution for powering up off-grid communities. However, this type of application requires the use of energy storage systems (ESS) to manage the intermittency of PV production. The most commonly used ESSs are lithium-ion batteries (Li-ion), but this technology has a low lifespan, mostly caused by the imposed stress. To reduce the stress on Li-ion batteries and extend their lifespan, hybrid energy storage systems (HESS) began to emerge. Although the utilization of HESSs has demonstrated great potential to make up for the limitations of Li-ion batteries, a proper power management strategy is key to achieving the HESS objectives and ensuring a harmonized system operation. This paper proposes a novel power management strategy based on an artificial neural network for a standalone PV system with Li-ion batteries and super-capacitors (SC) HESS. A typical standalone PV system is used to demonstrate and validate the performance of the proposed power management strategy. To demonstrate its effectiveness, computational simulations with short and long duration were performed. The results show a minimization in Li-ion battery dynamic stress and peak current, leading to an increased lifespan of Li-ion batteries. Moreover, the proposed power management strategy increases the level of SC utilization in comparison with other well-established strategies in the literature.