The superficial white matter (SWM) lies directly underneath the cortical ribbon and contains the short association fibers, or U-fibers, that connect neighboring gyri. Connectivity of these U-fibers is important for various neuroscientific research from the development to the aging of the brain. Nonetheless, conventional tractography methods can only provide a partial representation of these connections. Moreover, previous studies on U-fibers mainly extract tracts based on their shape characteristics without imposing the biologically critical condition that they should tightly follow the cortical surface. In this work we leverage the high resolution diffusion imaging data from the Human Connectome Project (HCP), and develop a novel surface-based framework for reconstructing the U-fibers. Guided by the projected fiber orientation distributions (FODs) on cortical surfaces, our method tracks the U-fibers from sulcal seed regions to neighboring gyrus on the triangular mesh representation of the cortex. Compared to volume-based tractography, the main advantage of our method is that it is intrinsic to the cortical geometry. More specifically, we define a novel approach for measuring the change of angles on the tangent space of the surface and use them to determine the U-fiber passing through a sulcal seed point. In experimental results, we compare our surface-based method with state-of-the-art FOD-based tractography from MRtrix on a large-scale dataset of 484 HCP subjects, and demonstrate that our method clearly achieves superior performance on the reconstruction of U-fibers between the precentral and postcentral gyrus.