With the development of vehicular ad-hoc networks (VANETs) and Internet of vehicles (IoVs), a large amount of useful information is generated for vehicle drivers and traffic management systems. The amount of vehicle and traffic information is as large as the number of vehicles and it is enormous when compared to vehicle calculation and storage performance. To resolve this problem, VANET uses a combined cloud computing technology, called vehicular cloud computing (VCC), which controls vehicle-related data, and helps vehicle drivers directly or indirectly. However, VANETs remain vulnerable to attacks such as tracking, masquerade and man-in-the-middle attacks because VANETs communicate via open networks. To overcome these issues, many researchers have proposed secure authentication protocols for message confirmation with vehicular cloud computing. However, many researchers have pointed out that some proposed protocols use ideal tamper-proof devices (TPDs). They demonstrated that realistic TPDs cannot prevent adversaries attack. Limbasiya et al. presented a message confirmation scheme for vehicular cloud computing using a realistic TPD in order to prevent these problems. However, their proposed scheme still has security weaknesses over a TPD and does not guarantee mutual authentication. This paper proposes a secure key agreement and authentication protocol to address the security weaknesses inherent in the protocol of Limbasiya et al. The suggested protocol withstands malicious attacks and ensures secure mutual authentication for privacy-preserving. We prove that the proposed protocol can provide session key security using Real-Or-Random (ROR) model. We also employed Automated Validation of Internet Security Protocols and Applications (AVISPA) simulation tool to show that the proposed protocol is able to defeat replay and man-in-the-middle attacks. Furthermore, we established that the proposed protocol can resist other malicious attacks by conducting the informal security analysis. We proved that our proposed protocol is lightweight and suitable for VCC environments.