Automatic dependent surveillance-broadcast (ADS-B) has become a crucial part of next generation air traffic surveillance technology and will be mandatorily deployed for most of the airspaces worldwide by 2020. Each aircraft equipped with an ADS-B device keeps broadcasting plaintext messages to other aircraft and the ground station controllers once or twice per second. The lack of security measures in ADS-B systems makes it susceptible to different attacks. Among the various security issues, we investigate the integrity and authenticity of ADS-B messages. We propose a new framework for providing ADS-B with authentication based on three-level hierarchical identity-based signature (HIBS) with batch verification. Previous signature-based ADS-B authentication protocols focused on how to generate signatures efficiently, while our schemes can also significantly reduce the verification cost, which is critical to ADS-B systems, since at any time an ADS-B receiver may receive lots of signatures. We design two concrete schemes. The basic scheme supports partial batch verification and the extended scheme provides full batch verification. We give a formal security proof for the extended scheme. Experiment results show that our schemes with batch verification are tremendously more efficient in batch verifying $n$ signatures than verifying $n$ signatures independently. For example, the running time of verifying 100 signatures is 502 and 484 ms for the basic scheme and the extended scheme respectively, while the time is 2500 ms if verifying the signatures independently.