Although high angular resolution diffusion MRI techniques are able to solve multiple intra-voxel fiber orientations, the usual streamline Diffusion Spectrum Imaging (DSI) tractography algorithms present some limitations in their ability to map complex fiber-crossings in the brain white matter because they select locally only the most linear trajectories. In this work, we present a fast marching tractography algorithm for DSI, called Fast-TraC, which 1) is able to efficiently address this issue, 2) creates fiber trajectories between 1000 small cortical ROIs covering the entire brain and 3) builds a whole brain connection matrix. We also see selected tracts that are accurately reconstructed.