The problem of non-preemptive scheduling of real-time periodic tasks with specified release times on a uniprocessor system is known as NP-hard problem. In this paper we propose a new non-preemptive scheduling algorithm and a new static scheduling strategy which use the repetitiveness and the predictability of periodic tasks in order to improve schedulabilities of real-time periodic tasks with specified release times. The proposed scheduling algorithm schedules periodic tasks by using the heuristic that precalculates if the scheduling of the selected task leads to the case that a task misses a deadline when tasks are scheduled by the non-preemptive EDF algorithm. If so, it defers the scheduling of the selected task to avoid the precalculated deadline-missing. Otherwise, it schedules the selected task in the same way as the non-preemptive EDF algorithm. Our scheduling algorithm can always find a feasible schedule for the set of periodic tasks with specified release times which is schedulable by the non-preemptive EDF algorithm. Our static sheduling strategy transforms the problem of non-preemptive scheduling for periodic tasks with specified release times into one with same release times for all tasks. It suggests dividing the given problem into two subproblems, making a non-preemptive scheduling algorithm to find two feasible subschedules for the two subproblems in the forward or backward scheduling within specific time intervals, and then combining the two feasible subschedules into a complete feasible schedule for the given problem. We present the release times as a function of periods for the efficient problem division. Finally, we show improvements of schedulabilities of our scheduling algorithm and scheduling strategy by simulation results.