The human cerebral cortex is a highly convoluted structure composed of sulci and gyri, corresponding to the valleys and ridges of the cortical surface respectively. Automatic parcellation of the cortical surface into sulcal regions is of great importance in structural and functional mapping of the human brain. In this paper, a novel method is proposed for automatic cortical sulcal parcellation based on the geometric characteristics of cortical surface including its principal curvatures and principal directions. This method is composed of two major steps: 1) employing the hidden Markov random field model (HMRF) and the expectation maximization (EM) algorithm on the maximum principal curvatures of the cortical surface for sulcal region segmentation, and 2) using a principal direction flow field tracking method on the cortical surface for sulcal basin segmentation. The flow field is obtained by diffusing the principal direction field on the cortical surface mesh. A unique feature of this method is that the automatic sulcal parcellation process is quite robust and efficient, and is independent of any external guidance such as atlas-based warping. The method has been successfully applied to the inner cortical surfaces of twelve healthy human brain MR images. Both quantitative and qualitative evaluation results demonstrate the validity and efficiency of the proposed method.