The electronic structures, magnetic properties, and half-metallicity of the MnTiZ (Z = S, Se, Te) half-Heusler compounds have been investigated by the first-principles calculations based on the density functional theory. Based on the calculated results, the MnTiZ (Z = S, Se, Te) half-Heusler compounds are predicted to be half-metallic ferrimagnet with a spin magnetic moment of 1 mu (B)/f.u., consistent with the Slater-Pauling rule. The magnetic moments of Mn and Ti are antiparallel to each other, which indicates ferrimagnetism in the MnTiZ (Z = S, Se, Te) compounds. It is also found that the lattice distortion affects the half-metallic properties of the MnTiZ (Z = S, Se, Te) compounds. Spin polarization over 99 % can be retained in the range of 5.55-5.75 for MnTiS, 5.60-5.85 for MnTiSe, and 5.80-6.20 for MnTiTe, respectively.