The recognition of sulcal regions on the cortical surface is an important task to shape analysis and landmark detection. However, it is challenging especially in a complex, rough human cortex. In this paper, we focus on the extraction of sulcal curves from the human cortical surface. The previous sulcal extraction methods are time-consuming in practice and often have a difficulty to delineate curves correctly along the sulcal regions in the presence of significant noise. Our pipeline is summarized in two main steps: 1) We extract candidate sulcal points spread over the sulcal regions. We further reduce the size of the candidate points by applying a line simplification method. 2) Since the candidate points are potentially located away from the exact valley regions, we propose a novel approach to connect candidate sulcal points so as to obtain a set of complete curves (line segments). We have shown in experiment that our method achieves high computational efficiency, improved robustness to noise, and high reliability in a test-retest situation as compared to a well-known existing method.