Since Vehicular ad hoc networks (VANETs) are vulnerable to various kinds of attacks, there is a need to fulfill the security requirements like message privacy, integrity, and authentication. The authentication technique is said to be efficient if it detects compromised nodes accurately with less complexity, reduced authentication delay, and keying overhead. In this paper, a trust-based authentication scheme for cluster-based VANETs is proposed. The vehicles are clustered, and the trust degree of each node is estimated. The trust degree is a combination of direct trust degree and indirect trust degree. Based on this estimated trust degree, cluster heads are selected. Then, each vehicle is monitored by a set of verifiers, and the messages are digitally signed by the sender and encrypted using a public/ private key as distributed by a trusted authority and decrypted by the destination. This verifies the identity of sender as well as receiver thus providing authentication to the scheme. By simulation results, we prove that the proposed technique provides high security with less overhead and delay.