The wide usage of embedded systems has affected their hardware and software significantly. The demands of new application, increasing amount of processing and the growth of technology encourages manufacturer to more powerful and high quality processors in such systems. The trend in growth of the personal computers toward heterogeneous processor, now has affected the modern embedded systems. Today’s embedded systems often have more than one core per state of the art processor and are changing to heterogeneous ones. These changes began from hardware and happened so fast that caused a gap and maybe mismatching between the hardware and the operating systems that used to manage the resources on them, of course the usage of HMC have had such advantages that seems it would be a popular trend in these systems in the future. In this project we deal with the scheduling of periodic real-time tasks on the HMC that which the existence of deadline make the scheduling more sensitive. The proposed method is a combination of scheduling methods on non-real-time HMC and scheduling methods on homogeneous processor. At first we categorized the task sets into the groups equal to the number of cores, then we assign them to the most matched cores. Now in each group a local scheduler with many well-known polices can be used. In this project we used Round Robin as local policy. Finally, when the system goes under heavy burdens, some tasks can be moved from higher priority queue to lower priority queue. This movement can be done in just one direction. Therefore, if one of the lower queue face with the congestion we can’t move some tasks to other queues. The performance of this method measured regards to the context switch penalty that we extract from a real processor, SPARC64™ VI of the SunSystem, we compare the proposed method with two other methods; Pfair and extended EDF, on WCET benchmarks. The results showed that on average deadlines would be satisfied with 10 percent improvement. In the other hands, the system’s performance had no significant changes and it takes O(n) to be run. So regards to improvement in satisfying the deadlines and keeping the performance in an already same leverage with the same order of complexity, we would have a more efficient system. Key words Embedded systems, realtime tasks scheduling, heterogeneous multicore processor, context switch penalty.