In the future it is very likely that asymmetric multi-core processors (AMP) will be used because of their proposed power efficiency and higher performance. In order to use the device intelligently and efficiently, it is essential to exploit the heterogeneity of AMPs. To fully exploit AMP systems, intelligent scheduling of tasks or intelligent resource management becomes one of the critical issues. In this paper, an AMP system is emulated, SPEC CPU2006 benchmark applications are executed as tasks, and heuristic methods for task scheduling are designed. Tasks are independent, non-preemptive, and have deadline (hard real-time) constraints. They arrive aperiodically and task migration is enabled. The performance metric is the total number of tasks completed by their deadline. The heuristic methods that are designed are compared with classic methods and the naïve Linux scheduler. Experimental results show that our task scheduling method completed 2.8 times more tasks than the naïve Linux scheduler for the proposed AMP environment.