NAND flash memory has unique characteristics like as 'out-place-update' and limited lifetime compared with traditional storage systems. According to out-of-place update scheme, a number of invalid (or called dead) pages can be generated. In this case, garbage collection is needed to reclaim invalid pages. Because garbage collection results in not only erase operations but also copy operations of valid (or called live) pages to other blocks, many garbage collection techniques have proposed to reduce the overhead and to increase the lifetime of NAND Flash systems. This techniques sometimes select victim blocks including cold data for the wear leveling. However, most of them overlook the cost of selecting victim blocks including cold data. In this paper, we propose a garbage collection technique named CAPi (Cost Age with Proportion of invalid pages). Considering the additional overhead of what to select victim blocks including cold data, CAPi improves the response time in garbage collection and increase the lifetime in memory systems. Additionally, the proposed scheme also improves the efficiency of garbage collection by separating cold data from hot data in valid pages. In experimental evaluation, we showed that CAPi yields up to, at maximum, 73% improvement in lifetime compared with existing garbage collections.