Hair is one of the most challenging objects to reconstruct due to its micro-scale structure and a large number of repeated strands with heavy occlusions. In this paper, we present the first method to capture high-fidelity hair geometry with strand-level accuracy. Our method takes three stages to achieve this. In the first stage, a new multi-view stereo method with a slanted support line is proposed to solve the hair correspondences between different views. In detail, we contribute a novel cost function consisting of both photo-consistency term and geometric term that reconstructs each hair pixel as a 3D line. By merging all the depth maps, a point cloud, as well as local line directions for each point, is obtained. Thus, in the second stage, we feature a novel strand reconstruction method with the mean-shift to convert the noisy point data to a set of strands. Lastly, we grow the hair strands with multi-view geometric constraints to elongate the short strands and recover the missing strands, thus significantly increasing the reconstruction completeness. We evaluate our method on both synthetic data and real captured data, showing that our method can reconstruct hair strands with sub-millimeter accuracy.