Conventional autonomous emergency braking (AEB) systems derive the relative distance of a curve using a curvature calculated through an in-vehicle sensor. However, as the AEB system cannot reflect geometric factors of a curve with variable curvature, it does not accurately estimate relative distances, based on which the AEB performance is evaluated. Accordingly, an AEB system reflecting the geometric information of curves needs to be considered and developed to improve the AEB performance for curves. This study proposes a method to improve the performance of AEB systems for curves through curvilinear coordinate conversion, which is used to reflect the geometric information of roads for the navigation of an autonomous vehicle. Both the host and target vehicles are located by means of curvilinear coordinate conversion. The positions thus identified are used to calculate the relative distance and lanes. Finally, the hazard risk criterion—that is, time-to-collision (TTC)—is derived using the proposed AEB system. To demonstrate the effectiveness of the proposed AEB system, this study compares it with the conventional AEB system by analyzing the collision avoidance performance on curves through relative distances and TTC.