In an asymmetric multi-core architecture, multiple heterogeneous cores share the last-level cache (LLC). Due to the different memory access requirements among heterogeneous cores, the LLC competition is more intense. In the current work, we propose a heterogeneity-aware replacement policy for the partitioned cache (HAPC), which reduces the mutual interference between cores through cache partitioning, and tracks the shared reuse state of each cache block within the partition at runtime to guide the replacement policy to keep cache blocks shared by multiple cores in multithreaded programs. In the process of updating the reuse state, considering the difference of memory accesses to LLC by heterogeneous cores, the cache replacement policy tends to keep cache blocks required by big cores, to better improve the LLC access efficiency of big cores. Compared with LRU and the SRCP, which are the state-of-the-art cache replacement algorithms, the performance of big cores can be significantly improved by HAPC when running multithreaded programs, while the impact on little cores is almost negligible, thus improving the overall performance of the system.