The traditional patch-based image completion algorithms circularly search the most similar patches in the whole image, and are easily affected by confidence factor in the process of structure propagation. As a result, these algorithms have poor efficiency and need a lot of time for the big computation. To overcome these shortages, a fast image completion algorithm based on randomized correspondence was proposed. It adopted a randomized correspondence algorithm to search the sample regions, which have similar structure and texture with the target region, so as to reduce the search space. Meanwhile, the method of computing filling priorities based on confidence factor and edge information was optimized to enhance the correctness of structure propagation. In addition, the method of calculating the most similar patches was improved. The experimental results show that, compared with the traditional algorithms, the proposed approach can obtain 5-10 times speed-up in repair rate, and performs better in image completion.