Map matching method is a fundamental preprocessing technique for massive probe vehicle data. Various transportation applications need map matching methods to provide highly accurate and stable results. However, most current map matching approaches employ elementary geometric or topological measures, which may not be sufficient to encode the characteristic of realistic driving paths, leading to inefficiency and inaccuracy, especially in complex road networks. To address these issues, this article presents a novel map matching method, based on the measure of curvedness of Global Positioning System (GPS) trajectories. The curvature integral, which measures the curvedness feature of GPS trajectories, is considered to be one of the major matching characteristics that constrain pairwise matching between the two adjacent GPS track points. In this article, we propose the definition of the curvature integral in the context of map matching, and develop a novel accurate map matching algorithm based on the curvedness feature. Using real-world probe vehicles data, we show that the curvedness feature (CURF) constrained map matching method outperforms two classical methods for accuracy and stability under complicated road environments.