In cognitive radio networks, cooperative spectrum sensing can improve the performance of spectrum utilization and accuracy of spectrum result. However, it suffers from security and privacy threats. Firstly, secondary users' sensing reports that have to be sent to the fusion center are heavily correlated to their locations, thereby leading to the leakage of locations of secondary users in the process of reports transmission and aggregation. Moreover, malicious secondary users are likely to submit fake sensing reports or alter sensing reports of other secondary users, which finally result in a wrong aggregated result. To address these questions, we propose an efficient location privacy-preserving authentication scheme for cooperative spectrum sensing. To be specific, our scheme incorporates a reputation mechanism and enables reliable secondary users to participate in cooperative spectrum sensing. Selected users with pseudo IDs instead of real identities send encrypted sensing reports to the fusion center. This can eliminate the correlation between sensing reports and secondary users and prevent the fusion center from associating sensing reports with secondary users' real identities while decrypting and aggregating reports, thereby protecting the location privacy of secondary users. Besides, to ensure a true aggregated result, we utilize elliptic curve cryptography technique to verify the legitimacy of sensing reports when the fusion center receives them. Theoretical analyses show that the proposed scheme protects the location privacy of secondary users. Numerical results demonstrate that the proposed scheme brings less overhead than previous schemes.