Nitride coatings improve the material properties of fiber in fiber-reinforced ceramic matrix composites, and in this study, we investigated the mechanical properties of (Ti0.875M0.125)N using ab initio calculation. We focused on the substitutional effect of a small amount of transition metal M (M=Cr, Hf, Mn, and Zr) in the titanium site. For the reliability of the data, it was set based on the model size and mechanical properties of known undoped ceramics. The shear and Young's modulus were the best in (Ti0.875Hf0.125)N solid solutions. CrN was the best among the whole compositions in bulk modulus, and (Ti0.875Mn0.125)N was the best among solid solutions in bulk modulus. The results of this study will provide useful information on how to develop nitrides as coating materials for fiber-reinforced ceramic matrix composites.