Half-metallic ferromagnet, in which the electrons with one spin band are metallic and the electrons with another spin band are semiconducting, is believed to be the most promising spin-injector material for spintronic devices, such as spin valves, spin filters, spin diodes, and magnetic tunnel junctions. The main advantages of half-metallic Heusler alloy over other half-metallic systems are their relatively high Curie temperatures and structural similarity to important binary semiconductors that are widely utilized in the industry. Thus far, half-metallicity has been predicted theoretically or confirmed experimentally in a limited number of Heusler alloys. Exploring new half-metallic Heusler alloys is necessary. In this study, the full-potential linearized augmented plane wave (FP_LAPW) method under density functional theory is utilized to investigate the electronic structures and magnetisms of semi-Heusler alloys CoCrTe and CoCrSb. In the calculations, the generalized gradient approximation (GGA) in the scheme of Perdew-Bueke-Ernzerhof is adopted to treat the exchange-correlation potential. The cutoff parameter is set to be Rmt Kmax =9, where Rmt is the smallest atomic sphere radius and Kmax is the maximum value of the reciprocal lattice vector. Meshes (131313 k-points) are used in the first Brillouin zone integration. Self-consistent calculations are considered to be convergent only when the integrated charge difference between the last two iterations is less than 110-4 e/cell. Spin-polarized calculations of the electronic structure for the semi-Heusler alloys CoCrTe and CoCrSb are performed. The calculations reveal that CoCrTe and CoCrSb at their equilibrium lattice constants are half-metallic ferromagnets with half-metallic gaps of 0.28 and 0.22 eV and total magnetic moments of 3.00 and 2.00 B per formula unit, respectively. The calculated integer total magnetic moments (in B) are consistent with the Slater-Pauling rule, Mt = Zt-18, where Zt denotes the total number of valence electrons and Mt means the total magnetic moment (in B) per formula unit. Moreover, the spin moment of the Cr atom is obviously larger than those of the Co, Te, and Sb atoms. Co, Te and Sb are all antiferromagnetically coupled to Cr for CoCrTe and CoCrSb. The electronic structures of CoCrTe and CoCrSb are also calculated as their lattice constants change from -13% to +13% relative to the equilibrium lattice constant. The calculated results indicate that CoCrTe and CoCrSb can maintain their half-metallicities and retain their total magnetic moments of 3.00 and 2.00 B per formula unit even as their lattice constants change from -11.4% to 9.0% and from -11.2% to 2.0%, respectively. The semi-Heusler alloys CoCrTe and CoCrSb should be useful in spintronics and other applications.