Existing collision avoidance methods for autonomous vehicles, which ignore the driving intent of detected vehicles, thus, cannot satisfy the requirements for autonomous driving in urban environments because of their high false detection rates of collisions with vehicles on winding roads and the missed detection rate of collisions with maneuvering vehicles. This study introduces an intent-estimation-and motion-model-based (IEMMB) method to address these disadvantages. First, a state vector is constructed by combining the road structure and the moving state of detected vehicles. A Gaussian mixture model is used to learn the maneuvering patterns of vehicles from collected data, and the patterns are used to estimate the driving intent of the detected vehicles. Then, a desirable long-term trajectory is obtained by weighting time and comfort. The long-term trajectory and the short-term trajectory, which are predicted using a constant yaw rate motion model, are fused to achieve an accurate trajectory. Finally, considering the moving state of the autonomous vehicle, collisions can be detected and avoided. Experiments have shown that the intent estimation method performed well, achieving an accuracy of 91.7% on straight roads and an accuracy of 90.5% on winding roads, which is much higher than that achieved by the method that ignores the road structure. The average collision detection distance is increased by more than 8 m. In addition, the maximum yaw rate and acceleration during an evasive maneuver are decreased, indicating an improvement in the driving comfort.