The energy existing in our environment can be converted into electricity to supply a wireless device such as sensor node. In this paper, we will address a problem of scheduling for a device that executes a mixed set of real-time tasks, composed of aperiodic and hard deadline periodic tasks. High responsiveness of the aperiodic tasks and timeliness of the periodic tasks can be performed through an aperiodic task server that takes into account both time and energy limitations. This paper describes an extension of the well known TBS (Total Bandwidth Server) which is energy harvesting aware. The performance of the new aperiodic server, called TB-H, is evaluated and compared to background approaches through simulation experiments.