Hashing methods have proven to be effective in the field of large-scale image retrieval. In recent years, the performance of hashing algorithms based on deep learning has greatly exceeded that of non-deep methods. However, most of the outstanding hashing methods are supervised models that heavily rely on annotated labels. In order to circumvent the huge overhead of labeling large-scale datasets, some unsupervised hashing algorithms have been proposed, such as pseudo labels and pseudo pairs. Since the image labels are strictly unavailable, some hyper-parameters in these methods are difficult to be selected, e.g., the final result is very sensitive to the picked number of categories or the chosen threshold of similarity for pairs. In addition, the calculation of pseudo-labels in high-dimensional space is not only computationally complex, but also has low precision. Therefore, in order to alleviate these issues in this paper, we propose a simple but effective Deep Unsupervised Self-evolutionary Hashing (DUSH) algorithm, which utilizes a curriculum learning strategy to iteratively select pseudo pairs from easy to hard in low dimensional Hamming space. Extensive experiments are conducted on four popular datasets, including two single-label datasets and two multi-label datasets, and the results show that our method can significantly outperform the state-of-the-art methods.