We report the result of first-principles calculations on the mechanism of the one-dimensional (1D) island formation on the hydrogen terminated Si(001)-(2 x 1) surface. It is found that the growth at the nonrebonded edge proceeds by capturing two surface Si adatoms and by releasing a H-2 molecule. The growth at the rebonded edge proceeds by capturing two surface Si adatoms and two surface H atoms. The growth at the nonrebonded edges is quicker than that at the rebonded edges. The number of islands having two rebonded edges are larger than those of other types of islands. These results are in good agreement with the experimental results.