UAV Ad-hoc Network (UANET) has been widely used in many fields. However, the collaborative communication and data sharing among multiple UAVs in UANET are often attacked and threatened, due to the limited software and hardware capability of UAVs and the openness of wireless network environment. In this work, we introduce blockchain technology into UANET to enhance its security. Instead of directly adopting traditional blockchain which require huge storage, computation and communication resources, we propose a lightweight reputation-based blockchain scheme for resource-constrained UANET, named AirBC. Firstly, we present a lightweight storage strategy by elimination and compression to reduce storage overhead for UAV nodes. Secondly, we propose an improved reputation-enhanced Practical Byzantine Fault Tolerance (PBFT) consensus, as well as a reputation evaluation scheme based on reliable recording of UAV behaviors. In our scheme, UAVs with high reputation are selected into a miner committee to perform the consensus, thus improving efficiency. Meanwhile, the committee is updated at regular intervals to ensure scalability of UANET. Thirdly, we adopt a weighted proposal voting scheme to enhance the ability of group decision-making for UANET. Finally, to evaluate our approach, simulations are conducted and their results demonstrate that AirBC can reduce 63% storage overhead and 69% consensus latency on average for different scale UANET.