Existing time series motif discovery algorithms have high computational complexity and cannot find multi-instance motifs. To overcome these defects, a Time Series motif discovery algorithm based on Subsequence full Joins and Maximum Clique (TSSJMC) was proposed. Firstly, the fast time series subsequence full join algorithm was used to obtain the distance between all subsequences and generate the distance matrix. Then, the similarity threshold was set, the distance matrix was transformed into the adjacency matrix, and the sub-sequence similarity graph was constructed. Finally, the maximum clique in the similarity graph was extracted by the maximum clique search algorithm, and the time series corresponding to the vertices of the maximum clique were the motifs containing most instances. In the experiments on public time series datasets, TSSJMC algorithm was compared with Brute Force algorithm and Random Projection algorithm which also could find multi-instance motifs in accuracy, efficiency, scalability and robustness. The experimental results demonstrate that compared with Random Projection algorithm, TSSJMC algorithm has obvious advantages in terms of efficiency, scalability and robustness; compared with Bruce Force algorithm, TSSJMC algorithm finds slightly less motif instances, but its efficiency and scalability are better. Therefore, TSSJMC is an algorithm that balances quality and efficiency.