First-principles calculations based on density functional theory (DFT) confirm the half-metallic ferromagnetism in both [Formula: see text] and [Formula: see text], and the nearly half-metallic ferromagnetism in [Formula: see text] Heusler alloys with the [Formula: see text]-type structure [Formula: see text]. The electronic band structures and density of states (DOS) calculations of the [Formula: see text] and [Formula: see text] compounds show that the spin-up electrons are metallic, whereas the spin-down bands are semiconducting with a gap of 0.47 eV and 0.53 eV, respectively, with 0.21 eV and 0.36 eV as a spin-flip gap, respectively. The [Formula: see text] and [Formula: see text] Heusler were half-metal compounds with magnetic moment of [Formula: see text] and [Formula: see text] at the equilibrium lattice constants [Formula: see text] Å and [Formula: see text] Å, respectively, which agrees with the Slater–Pauling rule, and have 100% polarization for a wide range of lattice parameters. The [Formula: see text] is a nearly half-metal (NHF) compound with magnetic moment of [Formula: see text] and 92.9% polarization at the equilibrium lattice constants [Formula: see text] Å and acquire half-metal behavior under the pressure 16.70 GPa.