High-precision location has become indispensable information in the era of Internet of Everything. However, the emergence of various location-based services leaves people exposed to the risk of location leakage at any time, which may cause potential safety hazards. This article is concerned with the issue of position privacy preserving in the range-based crowdsourcing localization system, where the location information of all involved members is protected from being disclosed by others, including the service provider. In order to maintain the mutual confidentiality of positions when exchanging information with each other, a method of secret sharing is used to hide the location-related input of each anchor by constructing it into a polynomial. Combined with a homomorphic encryption scheme, the estimated location of user can be kept secrecy to the service provider. The feasibility of the proposed protocol for the defined privacy protecting goals is proved. Numerical results demonstrate that our algorithm is superior in localization accuracy to the noise-adding based protocols, and has moderate computation and communication costs in contrast with the encryption-based strategies.