Vehicular Ad hoc Networks (VANETs) have gained considerable attention in recent years because of the extensive applications. However, VANETs are confronted with numerous difficulties and challenges, which lead to communication performance degradation and even data delivery failure. In this paper, we propose a new routing protocol called Intersection-based Delay sensitive Routing using Ant colony optimization (IDRA). Firstly, we derive a mathematical delay model for a two-lane road segment. Then based on proposed terminal intersection concept, IDRA makes use of Ant colony optimization (ACO) to find robust and optimal route with min-delay. The forward ants are in charge of exploring routes consisting of a succession of intersections, which are selected considering local road segment delay and global delay from current intersection to the terminal intersection of the destination. The backward ants take charge of collecting global delay and updating ant pheromone along the explored routes. Data packets are forwarded by dynamically choosing the next intersection utilizing updated ant pheromone. Greedy carry-and-forward mechanism is adopted by IDRA to forward data packets between two adjacent intersections, reducing the effects of individual vehicle movement on routing paths. Simulation results validate our derived road segment delay model and also indicate that IDRA shows better communication performance compared with an intersection-based geographical routing protocol (GSR) and a min-delay routing protocol (CAR).