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Heterogeneous Chip Multi-Processors (heter-CMP) provide suitable resources to various applications and could get more benefits on performance than homogeneous CMP. To fully develop the performance of the heter-CMP system, the applications should be scheduled to the proper cores by the scheduler of the operating system according to their behaviours. Besides, the last level cache (LLC) miss rate is often used as the metric to identify the application features. However, the LLC miss rate could not reflect the application behaviours accurately since the memory access delay, the most important application character is related to patterns of the memory access and many other issues. To improve the accuracy of scheduling on the heter-CMP system, this paper supplies performance counters for the LLC miss penalty to monitor application behaviours. Based on that, the latency-aware scheduling algorithm for asymmetry chip multi-processors (LA-ACMP) is proposed and implemented. Those hardware supports are implemented on the Godson-3 multi-core RTL and simulator and the LA-ACMP algorithm is integrated to the Linux kernel. The performance evaluation on those platforms shows that the LA-ACMP algorithm with LLC miss penalty outperforms the algorithm with LLC miss rate about 32.4%, and outperforms the original schedule algorithm about 18.4%.