Similarity range query over string sequences plays a significant role in bioinformatics, entity extraction, data mining and information retrieval. Meanwhile, with the popularity of cloud computing, a new paradigm is to outsource the similarity range query service to the cloud. However, existing solutions still have suffer from security and query efficiency drawbacks. To address these issues, we propose an efficient and private similarity range query scheme over encrypted string sequences. Specifically, we first organize string sequences into inverted index and design an inverted index based efficient similarity range query algorithm by applying several filter strategies. Second, based on public-key homomorphic encryption, we design a set of privacy-preserving protocols to protect the privacy of inverted index based range queries. Based on this, we propose a private and computationally efficient similarity range query scheme. Finally, we analyze the security of our scheme and conduct experiments to evaluate its performance, and the results indicate that our proposed scheme is computationally effective.