This paper presents a new aperiodic request server in real-time energy harvesting system. This server handles hard periodic tasks and soft aperiodic tasks, using ED-H in order to schedule periodic tasks. The main principle of the server is to minimize response times of aperiodic tasks without compromising the schedulability of periodic tasks. The server, known as SSP (Slack stealing with Energy Preserving), enhances the response time offered by the Slack stealing approach, because of idle times and energy surplus. Finally, performance evaluation is made by comparing the server with two background servers.