Compact hash codes can facilitate large-scale multimedia retrieval, significantly reducing storage and computation. Most hashing methods learn hash functions based on the data similarity matrix, which is predefined by supervised labels or a distance metric type. However, this predefined similarity matrix cannot accurately reflect the real similarity relationship among images, which results in poor retrieval performance of hashing methods, especially in multi-label datasets and zero-shot datasets that are highly dependent on similarity relationships. Toward this end, this study proposes a new supervised hashing method called supervised adaptive similarity matrix hashing (SASH) via feature-label space consistency. SASH not only learns the similarity matrix adaptively, but also extracts the label correlations by maintaining consistency between the feature and the label space. This correlation information is then used to optimize the similarity matrix. The experiments on three large normal benchmark datasets (including two multi-label datasets) and three large zero-shot benchmark datasets show that SASH has an excellent performance compared with several state-of-the-art techniques.