The Slater–Pauling behavior and half-metallic properties of full-Heusler alloys Mn 2 CuZ (Z=Ge and Sb) have been studied by first-principles calculations. It is found that the total spin moment (M t ) and the number of valence electrons (Z t ) follow a Slater–Pauling rule of M t =Z t −28 rather than M t =Z t −24 in normal Heusler alloys. Mn 2 CuSb is predicted to be a half-metal at equilibrium lattice constant and Mn 2 CuGe is also half-metallic with a small expansion of the lattice. Mn 2 CuGe and Mn 2 CuSb are both ferrimagnets with total spin moment of +0.97μ B /f.u. and +2.00μ B /f.u., respectively. Considering Mn 2 CuGe and Mn 2 CuSb have 29 and 30 valence electrons, the S-P curve of M t =Z t −28 works quite well. This different S-P rule is strongly related to the low-lying Cu states and the weak hybridization between the d states of Cu and Mn.