To achieve high storage saving, data deduplication techniques are widely used in many practical cloud storage services, which removes redundant data and keeps only a single copy of them. However, secure data deduplication over encrypted data is challenging since encryption may result in different ciphertexts even when the original messages are the same. Thus, message-locked encryption (MLE) is proposed to solve this issue and demonstrates that it is secure under the unpredictable message set. Since block-level deduplication can achieve more fine-grained storage saving, several block-level deduplication schemes that support updatability are also vividly proposed. However, the previous updatable block-level MLE schemes are vulnerable against brute-force attack when the message set is predictable. Since the size of a block is typically much less than an arbitrary size of a file, the predictability problem is a very important pragmatic concern which should be addressed in the block-level deduplication literature. In this paper, thus, we propose a novel secure block-level deduplication scheme that guarantees efficient data update and brute-force attack resilience even when messages are predictable with the rigorous security proof. Also, our performance evaluation shows that additional time and bandwidth usage can be minimized as the size of a block increases.