k-nearest neighbor (k-NN) query is widely applied to various networks, such as mobile Internet, peer-to-peer (P2P) network, urban road networks, and so on. The location-based service in the outsourced environment has become a research hotspot with the rise of cloud computing. Meanwhile, various privacy issues have been increasingly prominent. We propose an efficient privacy-preserving query protocol to accomplish the k-nearest neighbor (k-NN) query processing on outsourced data. We adopt the Moore curve to transform the spatial data into one-dimensional sequence and utilize the AES to encrypt the original data. According to the cryptographic transformation, the proposed protocol can minimize the communication overhead to achieve efficient k-NN query while protecting the spatial data and location privacy. Furthermore, the proposed efficient scheme offers considerable performance with privacy preservation. Experiments show that the proposed scheme achieves high accuracy and efficiency while preserving the data and location privacy when compared with the existing related approach.