The k-nearest neighbor (kNN) algorithm identifies points of interest (PoIs) in a dataset that are most similar to a given query point, and is widely applied in location-based query services. To enhance efficiency, such services are often outsourced to cloud servers. However, this outsourcing raises concerns about data privacy. In this paper, we propose a privacy-preserving kNN query scheme tailored for outsourced cloud environments. The scheme adopts a dual cloud server model, leveraging secret sharing to protect both the PoI dataset and user queries. To improve query efficiency, a kd-tree structure is employed. Furthermore, we design a secure Euclidean distance protocol and a comparison protocol, enabling the two cloud servers to collaboratively perform kNN queries over the shared kd-tree without revealing sensitive information. Security analysis shows that the proposed scheme effectively protects user location and query privacy. Experimental results demonstrate that our scheme achieves low computational and communication overhead, making it highly practical for real-world applications.