As there has been an advancement in avionic systems in recent years, the enactment of unmanned aerial vehicles (UAV) has upgraded. As compared to a single UAV system, multiple UAV systems can perform operations more inexpensively and efficiently. As a result, new technologies between user/control station and UAVs have been developed. FANET (Flying Ad-Hoc Network) is a subset of the MANET (Mobile Ad-Hoc Network) that includes UAVs. UAVs, simply called drones, are used for collecting sensitive data in real time. The security and privacy of these data are of priority importance. Therefore, to overcome the privacy and security threats problem and to make communication between the UAV and the user effective, a competent anonymous mutual authentication scheme is proposed in this work. There are several methodologies addressed in this work such as anonymous batch authentication in FANET which helps to authenticate a large group of drones at the same time, thus reducing the computational overhead. In addition, the integrity preservation technique helps to avoid message alteration during transmission. Moreover, the security investigation section discusses the resistance of the proposed work against different types of possible attacks. Finally, the proposed work is related to the prevailing schemes in terms of communication and computational cost and proves to be more efficient.