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In many real-time systems, there are not only periodic real-time tasks, but also aperiodic real-time tasks arising from arbitrary critical events. In this paper, we propose an algorithm (SATSS, Schedule Aperiodic Tasks on a Static Schedule) scheduling both periodic real-time tasks and aperiodic real-time tasks. This algorithm first produces a schedule which consists of only periodic tasks before the system is started and schedules aperiodic tasks on the static schedule on run time. It can guarantee all accepted tasks' deadlines by testing the schedulability of aperiodic tasks in a busy period consisting of not only the running tasks but also the periodic tasks in future. Experimental results show that the algorithm is effective.