Automatic parcellation of infant cortical surfaces into anatomical regions of interest (ROIs) is of great importance in brain structural and functional analysis. Conventional cortical surface parcellation methods suffer from two main issues: (1) Cortical surface registration is needed for establishing the atlas-to-individual correspondences; (2) The mapping from cortical shape to the parcellation labels requires designing of specific hand-crafted features. To address these issues, in this paper, we propose a novel cortical surface parcellation method, which is free of surface registration and designing of hand-crafted features, based on deep convolutional neural network (DCNN). Our main idea is to formulate surface parcellation as a patch-wise classification problem. Briefly, we use DCNN to train a classifier, whose inputs are the local cortical surface patches with multi-channel cortical shape descriptors such as mean curvature, sulcal depth, and average convexity; while the outputs are the parcellation label probabilities of cortical vertices. To enable effective convolutional operation on the surface data, we project each spherical surface patch onto its intrinsic tangent plane by a geodesic-distance-preserving mapping. Then, after classification, we further adopt the graph cuts method to improve spatial consistency of the parcellation. We have validated our method based on 90 neonatal cortical surfaces with manual parcellations, showing superior accuracy and efficiency of our proposed method.