We extend the recent study on above-room-temperature half-metallic ferromagnetism in bulk rocksalt CrTe [Y. Liu, S. K. Bose, and J. J. Kudrnovský, Phys. Rev. B 82, 094435 (2010)] to the (001) and (111) surfaces by using the first-principles calculations. We show that the Te-terminated (111) surface is energetically more stable than both the (001) and the Cr-terminated (111) surfaces over the whole effective Cr chemical potential, and the surface stability of the Te-terminated (111) surface of rocksalt CrTe is comparable with that of the Te-terminated (001) surface of experimental zinc-blende CrTe. In addition, both the (001) and (111) surfaces of rocksalt CrTe retain the bulk half-metallicity. The atomic magnetic moments at the (111) surfaces are greatly different from those in the bulk rocksalt CrTe due to the breakdown of Cr-Te bond at the (111) surface, but the differences are very small for the case of the (001) surface due to the existence of Cr-Te bond at the (001) surface. These results indicate that it is feasible to fabricate the half-metallic CrTe thin films with rocksalt structure other than zinc-blende one.