A wireless sensor network (WSN) that deploys an unmanned aerial vehicle (UAV) for the data gathering process differs from the common WSN system. In a UAV-WSN, the sensor nodes have a limited time to communicate with the UAV. Thus, the sensor nodes have to contend with each other to transmit their data to the UAV within a short amount of time. The fairness among the contended nodes is degraded, which affects the network performance in terms of the throughput and packet delivery ratio (PDR). This paper proposes a hybrid medium access control (MAC) protocol for data gathering in a UAV-WSN. The UAV periodically sends a beacon frame to inform sensor nodes of its presence. Each sensor node that receives the beacon frame contends to send a registration frame to the UAV. The UAV then transmits a second beacon frame to the registered nodes regarding their transmission schedule. The time-slot scheme is used to determine the transmission schedule of each sensor based on their priority during the registration process. This paper introduces the architecture of the UAV-WSN data gathering system and the results of simulations showing that the proposed MAC protocol achieved fairness while enhancing the network performance in terms of PDR and throughput.