As location-based services (LBS) are widely used in vehicular ad-hoc networks (VANETs), location privacy has become an utmost concern. Spatial cloaking is a popular location privacy protection approach, which uses a cloaking area containing k-1 collaborative vehicles (CVs) to replace the real location of the requested vehicle (RV). However, all CVs are assumed as honest in k-anonymity, and thus giving opportunities for dishonest CVs to submit false location information during the cloaking area construction. Attackers could exploit dishonest CVs' false location information to speculate the real location of RV. To suppress this threat, an edge-assisted Trusted Collaborative Anonymity construction scheme called TCA is proposed with trust mechanism. From the design idea of trusted observations within variable radius r, the trust value is not only utilized to select honest CVs to construct a cloaking area by restricting r's search range but also used to verify false location information from dishonest CVs. In order to obtain the variable radius r of searching CVs, a multiple linear regression model is established based on the privacy level and service quality of RV. By using the above approaches, the trust relationship among vehicles can be predicted, and the most suitable CVs can be selected according to RV's preference, so as to construct the trusted cloaking area. Moreover, to deal with the massive trust value calculation brought by large quantities of LBS requests, edge computing is employed during the trust evaluation. The performance analysis indicates that the malicious response of TCA is only 22% of the collaborative anonymity construction scheme without trust mechanism, and the location privacy leakage is about 32% of the traditional Enhanced Location Privacy Preserving (ELPP) scheme.