In this work, we exploit the T1 weighted image in conjunction with cortical surface boundary to improve the precision of tractography under the cortex. We show that utilizing the cortical interface and a surface flow, to model the superficial white matter streamlines, enhance and improve tractography trajectory near the cortex. Our novel surface-enhanced tractography reduces the gyral bias, the length bias and the amount of false positive streamlines produced by tractography. This method improves the reproducibility and the cortical surface coverage of tractograms which are crucial for connectomics studies. The usage of cortical surfaces, extracted from the standardly acquired 1 mm isotropic T1, is a straightforward and effective way to improve existing tractography processing pipelines and structural connectivity studies.