Cloud service providers adopt a deduplication technique to minimize resource utility costs. However, it is one of the most challenging issues to manage the outsourced data in a storage-efficient way when users encrypt data for preserving privacy and frequently update it. When the data is updated, file-level deduplication makes entire copy of updated file although there are small modifications. Block-level deduplication solves this problem, but it requires metadata larger than the outsourced blocks. To address this problem, we propose a hybrid deduplication scheme that minimizes storage overhead. Our scheme performs filelevel deduplication along with isolation of only updated blocks with augmented metadata. The analysis results show that our scheme minimizes storage costs while guaranteeing secure update with efficient verification.