The quantity of data in real-world applications is growing significantly while the data quality is still a big problem. Similarity search and similarity join are two important operations to address the poor data quality problem. Although many similarity search and join algorithms have been proposed, they did not utilize the abilities of modern hardware with multi-core processors. It calls for new parallel algorithms to enable multi-core processors to meet the high performance requirement of similarity search and join on big data. To this end, in this paper we propose parallel algorithms to support efficient similarity search and join with edit-distance constraints. We adopt the partition-based framework and extend it to support parallel similarity search and join on multi-core processors. We also develop two novel pruning techniques. We have implemented our algorithms and the experimental results on two real datasets show that our parallel algorithms achieve high performance and obtain good speedup.