With the rapid miniaturization in sensor technology, Internet-of-Drones (IoD) has delighted researchers towards information transmission security among drones with the control station server (CSS). In IoD, the drone is different in shapes, sizes, characteristics, and configurations. It can be classified on the purpose of its deployment, either in the civilian or military domain. Drone’s manufacturing, equipment installation, power supply, multi-rotor system, and embedded sensors are not issues for researchers. The main thing is to utilize a drone for a complex and sensitive task using an infrastructure-less/self-organization/resource-less network type called Flying Ad Hoc Network (FANET). Monitoring data transmission traffic, emergency and rescue operations, border surveillance, search and physical phenomenon sensing, and so on can be achieved by developing a robust mutual authentication and cross-verification scheme for IoD deployment civilian drones. Although several protocols are available in the literature, they are either design issues or suffering from other vulnerabilities; still, no one claims with conviction about foolproof security mechanisms. Therefore, in this paper, the researchers highlighted the major deficits in prior protocols of the domain, i.e., these protocols are either vulnerable to forgery, side channel, stolen-verifier attacks, or raised the outdated data transmission flaw. In order to overcome these loopholes and provide a solution to the existing vulnerabilities, this paper proposed an improved and robust public key infrastructure (PKI) based authentication scheme for the IoD environment. The proposed protocol’s security analysis section has been conducted formally using BAN (Burrows-Abadi-Needham) logic, ProVerif2.03 simulation, and informally using discussion/pragmatic illustration. While the performance analysis section of the paper has been assessed by considering storage, computation, and communication cost. Upon comparing the proposed protocol with prior works, it has been demonstrated that it is efficient and effective and recommended for practical implementation in the IoD environment.