The structural, electronic, and magnetic properties of the full-Heusler compounds Co2MnZ (Z = Al, Ge, Si, Ga) have been investigated using the first-principles calculations with the full-potential linear-augmented plane wave method within the density functional theory. The electronic structures and magnetic properties of the Co2MnZ (Z = Al, Ge, Si, Ga) compounds with both Hg2CuTi- and Cu2MnAl-type structures are studied. It is found that the calculated lattice constants are in good agreement with the theoretical values. Using the general gradient approximation, we observe that the Cu2MnAl-type structure is more stable than the Hg2CuTi type. The Co2MnZ (Z = Al, Ge, Si, Ga) compounds were half-metallic ferromagnets in the Cu2MnAl-type structure. The total magnetic moments of the Co2MnZ (Z = Al, Ge, Si, Ga) compounds in the Cu2MnAl-type structure were 4, 5, 5, and 4 μB, respectively, which is in agreement with the Slater-Pauling rule, m = NV−24 Furthermore, the origin for the appearance of the half-metallic band gap in the Co2MnZ compound was also discussed which shows them to be promising materials for possible spintronics applications.