The evolution of Flying Ad-hoc Networks (FANETs) marks the paradigm shift from a single large drone to multiple small drones linked together in an ad-hoc fashion. To maintain the Quality of Service (QoS) in the multi-hop networking schema, FANETs utilize the available resources efficiently. However, due to open wireless boundary and high mobility of the drones, the FANETs are vulnerable to malicious nodes that can penetrate the network and, thus, pose serious security threats, particularly at the Medium Access Control (MAC) layer. Such susceptibility compromises the network security and privacy and harms the information exchange operation within the network. The attacker can either transmit a large number of reservation requests to waste the bandwidth, listen to the control messages, conduct power-efficient jamming or falsify the information to manipulate the network control. Therefore, secure access control and a key agreement mechanism are required. The mechanism must utilize the two phases, i.e., node authentication and key agreement, to counter the aforementioned attacks. Our contribution, in this paper, is a certificate-based access control and key agreement scheme, which is based on the technique of Hyperelliptic Curve Cryptography (HECC) and employs a collision-resistant one-way cryptographic hash function. In order to assess the viability and performance of the proposed scheme, we analyze it using formal security analysis techniques, such as the Real-Or-Random (ROR) model and Automated Validation of Internet Security Protocols and Applications (AVISPA) tool. The scheme is also evaluated using the informal security analysis technique, or the nonmathematical approach. The results obtained from both analyses affirm the superiority of our proposed scheme.