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Increasing number of processor cores on a chip is a driving force to move to three-dimensional integration. On the other hand, as the number of processor cores increases, non-uniform cache architecture (NUCA) receives growing attention. Reducing effective memory access time, including cache hit time and miss penalty, is crucial in such multi-processor systems. In this paper, we propose a Latency-aware Utility-based Cache Partitioning (LUCP) method which reduces memory access time in a 3D-stacked NUCA. To reduce the memory access time, the proposed method partitions shared NUCA cache for each processor core according to latency variation (depending on the physical distance from processor core to cache bank) and cache access characteristic of application programs. Experimental results show that the proposed method reduces memory access time by up to 32.6% with an average of 14.9% compared to conventional method.