Protecting location privacy of mobile systems is important for various location-based services in pervasive computing scenarios. How to quickly compute the target user's location without knowing each anchor user's location has drawn much attention. Under the classical nonadjacent subtraction based localization model, existing solutions based on homomophic encryption introduce much computation and communication overheads to achieve privacy-preserving localization. In this paper, an adjacent subtraction based localization model is proposed, which is suitable to efficiently protect users' privacy. Then, under such a model, an efficient privacy-preserving localization algorithm is developed without using homomophic encryption. A closed-form expression of the relationship between the localization error and the measurement noise is derived. Furthermore, a comprehensive analysis, including correctness analysis, privacy analysis, and efficiency analysis, is presented. Some simulations are conducted to show that the proposed model has equivalent accuracy and efficiency with the classical model. Some numerical results are presented to show the efficiency of the proposed privacy-preserving localization algorithm.