Vehicular ad-hoc networks (VANETs) consist of highly mobile and self-organized nodes that wirelessly communicate with one another and transmit a variety of information, some of which may be critical information. Due to the rapidly changing topology of VANETs and the high-speed mobility of the participating vehicles, the routing of packets in these networks is a challenging task. Moreover, the presence of malicious vehicles in VANETs makes the correct routing of packets more challenging. In this paper, we propose a trust-based geographic routing protocol for VANETs (TGRV) that limits the participation of malicious vehicles in routing. In TGRV, to select the next-hop, a sender not only considers the distance, speed, and direction of its neighbors but also evaluates their direct trust and recommendation trust. For this purpose, TGRV uses a monitoring system that allows each vehicle to monitor the correct packet forwarding rate of its next-hop. In this way, the vehicle updates its direct trust to the next-hop and retransmits the packets if the packets are lost. The vehicle also sends its observations of the next-hop to its neighbors with a push-based notification, and based on that, the neighbors can update their recommendation trust about the next-hop. The monitoring system applies distance prediction in a modified promiscuous mode to better estimate the correct packet forwarding rate of the next-hop. To enhance the accuracy of trust management, the trust values of interactions are reduced over time by using a decay factor. TGRV uses the number and trust of two-hop neighbors, which helps in selecting the next-hop that is in a more trusted zone. Our extensive simulations on OMNeT++ show that when the percentage of malicious vehicles in an urban scenario increases from 0 to 25%, the packet delivery ratio of TGRV decreases from 95.1 to 88.7%, which performs very well compared to the GPSR and PGRP protocols. Also, the end-to-end delay of TGRV increases from 3.79 to 7.07 s and the average hop count of TGRV increases from...