A first-principles approach based on the density functional theory (DFT) was used to study the electronic structure and magnetism of CoRhYZ (Y = Sc, Ti, Cr, and Mn; Z = Al, Si, and P). The results showed that among these compounds CoRhCrSi CoRhMnSi, CoRhCrAl and CoRhTiAl were true half-metallic ferromagnets in the stable structure of Y (I) Half metallicity mainly originated from d-d and covalent hybridizations between transition metals. The total magnetic moment of the four half-metallic compounds follows the conventional Slater-Pauling rule: M (tot) = Z (tot) - 24 Half metallicity is quite robust against hydrostatic strain and CoRhCrSi, CoRhMnSi, CoRhTiAl, and CoRhCrAl compounds maintained the half-metallic character at ranges of 5.47-6.02, 5.56-6.02, 5.98-6.54, and 5.48-5.92 , respectively. Therefore, these compounds were ideal candidates for spintronic applications.