This paper proposes a new MAC protocol that is used for a wireless sensor network employing one Unmanned Aerial Vehicle (WSN-UAV). In this protocol, the active sensors are classified into different groups with different priorities that are controlled by the UAV. The level of priorities is closely dependent on the receiving power of the beacon signal at the sensors and the variation trend of this receiving power value. The proposed MAC protocol assures a certain Packet-Error-Rate (PER) by selecting a proper number of transmitting groups that is equal or less than the number of priority groups. As a result, only the active sensors that are located inside the transmitting groups will periodically transmit their sensing data to the UAV. CDMA will be used for data transmission between the sensors and the UAV as an effective method. The results show that, the larger number of transmitting groups the smaller value of time needed for data collection and the higher value of PER; or inversely. This paper therefore aims to find a relation among the three factors: the number of transmitting groups, the acceptable PER and the average time for data collection.