In cloud computing, secure analysis on outsourced encrypted data is a significant topic. As a frequently used query for online applications, secure k-nearest neighbors (k-NN) computation on encrypted cloud data has received much attention, and several solutions for it have been put forward. However, most existing schemes assume the query users are fully trusted and all query users share the total key which is used to encrypt and decrypt data owner's outsourced data. It is constitutionally not feasible in lots of real-world applications. In this paper, we propose a novel secure and efficient scheme for k-NN query on encrypted cloud data in which the key of data owner to encrypt and decrypt ousourced data will not be completely disclosed to any query user. Therefore, our scheme can efficiently support the secure k-NN query on encrypted cloud data even when query users are not trustworthy enough.