Internet of Vehicles (IoV) is an intelligent application of Internet of Things (IoT) in smart transportation that takes intelligent commitments to the passengers to improve traffic safety and efficiency, and generate a more enjoyable driving and riding environment. Fog cloud-based IoV is another variant of mobile cloud computing where vehicular cloud and Internet can co-operate in more effective way in IoV. However, more increasing dependence on wireless communication, control, and computing technology makes IoV more dangerous to prospective attacks. For secure communication among vehicles, road-side units, fog and cloud servers, we design a secure authenticated key management protocol in fog computing-based IoV deployment, called AKM-IoV. In the designed AKM-IoV, after mutual authentication between communicating entities in IoV they establish session keys for secure communications. AKM-IoV is tested for its security analysis using the formal security analysis under the widely accepted real-or-random (ROR) model, informal, and formal security verification using the broadly accepted automated validation of Internet security protocols and applications (AVISPAs) tool. The practical demonstration of AKM-IoV is shown using the NS2 simulation. In addition, a detailed comparative study is conducted to show the efficiency and functionality and security features supported by AKM-IoV as compared to other existing recent protocols.