By using the highly precise all-election full potential linearized augmented plane-wave method based on density functional theory within the generalized gradient approximation, we investigated magnetocrystalline anisotropy and magnetism of zinc-blende CrTe (001) surface. We observed that both of the Cr- and Te-terminated zinc-blende CrTe (001) surfaces maintain the half-metallicity by analyzing the density of states. The magnitudes of the calculated magnetic moments for the Cr(S) and Cr(S-1) atoms are calculated to be 3.92 and 3.16 mu(B) for the Cr- and Te-terminated surfaces, respectively. The Te atoms show significantly induced negative spin polarizations of 0.13-0.30 mu(B). The spin orientations at the Te-terminated (Cr-terminated) surfaces were found to be in-plane (out-of-plane) regardless of its thickness. Since a Te-terminated surface is known as to be more stable than a Cr-terminated one, our result is consistent with an experiment which observed in-plane magnetic anisotropy at a CrTe (001) surface. (C) 2011 Elsevier B.V. All rights reserved.