Using the first-principles density functional theory, we calculate the crystal structures, magnetisms and electronic structures of Sb-containing half-Heusler alloys XYSb(X=Ni, Pd, Pt; Y=Mn, Cr). The calculation results show that alloy NiMnSb is half-metal and the others are metals at equilibrium lattice constant. The contribution of the spin magnetic moment of Y element to the total moment is largest for all alloys. It is found that the Fermi level of the minority spin band shifts closer to the bottom of spin-down conduction band with atomic number of X element reducing. The Fermi level moves up due to the compressive strain, away from p bands of Sb atom. Under the compresive stress, PtMnSb, PdMnSb and NiCrSb can induce metal half-metal transitions.