By means of Monte Calro simulation we study step bunching induced by the drift of adatoms with anisotropic surface diffusion. Like a vicinal face of Si(001), we suppose that two types of terraces appear alternately, and their directions of fast diffusion are parallel and perpendicular to the steps. When the drift is perpendicular to the steps, we found from stability analysis that the vicinal face is unstable for pairing instability with both step-up and step-down drift. In a late stage of bunching, large bunches appear irrespective of the drift direction, while formation process of the bunches is affected by the drift direction. (C) 2002 Elsevier Science B.V. All rights reserved.