The last decade has witnessed a tremendous growth of service computing, while efficient service recommendation methods are desired to recommend high-quality services to users. It is well known that collaborative filtering is one of the most popular methods for service recommendation based on QoS, and many existing proposals focus on improving recommendation accuracy, i.e., recommending high-quality redundant services. Nevertheless, users may have different requirements on QoS, and hence diversified recommendation has been attracting increasing attention in recent years to fulfill users' diverse demands and to explore potential services. Unfortunately, the recommendation performances relies on a large volume of data (e.g., QoS data), whereas the data may be distributed across multiple platforms. Therefore, to enable data sharing across the different platforms for diversified service recommendation, we propose a Privacy-preserving Diversified Service Recommendation (PDSR) method. Specifically, we innovate in leveraging the Locality-Sensitive Hashing (LSH) mechanism such that privacy-preserved data sharing across different platforms is enabled to construct a service similarity graph. Based on the similarity graph, we propose a novel accuracy-diversity metric and design a $2$-approximation algorithm to select $K$ services to recommend by maximizing the accuracy-diversity measure. Extensive experiments on real datasets are conducted to verify the efficacy of our PDSR method.