Cloud computing brought a shift from the traditional clientserver model to DataBase as a Service (DBaaS), where the data owner outsources her database as well as the data management function to the cloud service provider. Although cloud services relieve the clients from the data management burdens, a significant concern about the data privacy remains. In this work, we focus on privacy-preserving k-nearest neighbour (k-NN) query, and provide the first sublinear solution (with preprocessing) with computational complexity Õ (klog4n) in the honestbut- curious adversarial setting. Our constructions use the data structure called kd-tree to achieve sublinear query complexity. In order to protect data access patterns, garbled circuits are used to simulate Oblivious RAM (ORAM) for accessing data in the kd-tree. Compared to the existing solutions, our scheme imposes little overhead on both the data owner and the querying client.