The data gathering process deploying Unmanned Aerial Vehicles (UAVs) in Wireless Sensor Networks (WSNs) is different from the common WSN system. In UAV-WSN, The ground nodes only have a limited time to communicate with the UAV. It makes the ground nodes to contend among each other to transmit their data to the UAV within a short time. Therefore, the fairness among the contended nodes is degraded that affected the network performance such as throughput and Packet Delivery Ratio (PDR). In this work, a novel MAC protocol for data gathering in UAV-WSN is proposed. The proposed MAC protocol uses four states mechanism to maintain the fairness and the energy consumption of nodes. The proposed MAC protocol uses deterministic backoff mechanism instead of Binary Exponential Backoff (BEB) to avoid the collision among contended nodes. Simulation results verify that this proposed MAC protocol enhances the network performance of the system in term of throughput, Packet Delivery Ratio (PDR), and fairness.