As the demand for electronic devices increases continually, the spintronic materials have played an important role in materials science and electronics. Spintronic devices have excellent properties such as non-volatility, low power consumption, and high integration compared with conventional semiconductor devices. In this paper, we investigate the electronic structure, magnetic and optical properties of the semiconductor GaSb doped with 3d transition metal Cr, based on first-principles calculations. The compounds are constructed by replacing some Ga atoms with Cr in zinc-blende GaSb semiconductor, where the concentrations of the Ga atoms replaced are 0, 0.25, 0.50, and 0.75. We adopt the projected plane wave method and the electronic exchange correlation functional PBE in the generalized gradient approximation. Band gap is modified by Heyd-Scuseria-Ernzerhof (HSE06) functional. We study the equilibrium lattice constants of Cr-doped GaSb in zinc-blende structure at different concentrations. The energy of nonmagnetic, ferromagnetic and antiferromagnetic states at the equilibrium lattice constants are compared to identify the ground state. For Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75), we find that the most stable state is ferromagnetic state. In the electronic structure of the ground state, the spin-up bands pass through the Fermi level while the spin-down bands each have a direct band gap. The Ga_1–xCr_xSb exhibit ferromagnetic half-metallic properties. The magnetic properties at different lattice constants under different concentrations are studied. Our analysis indicates that the Ga_1–xCr_xSb have integer Bohr magnetic moments of 3.0, 6.0, 9.0 μ_B for x = 0.25, 0.50 and 0.75, respectively. We find that when the lattice changes fom –5% to 20%, the total magnetic moment for each of Ga_1–xCr_xSb still remains the integer Bohr magnetic moment, and the magnetic moment of the Cr increases with the lattice constant increasing. We also find that the ferromagnetisms of Ga_1–xCr_xSb have Curie temperatures above room temperature, estimated by mean-field method. The p-d electron hybridization occurs in Cr-3d orbital and Sb-5p orbital, and the electron state density distribution of Cr-3d is transferred, that is, the electron orbital hybridization makes the total electron state density of crystal material redistributed, which is the main reason why Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75) present ferromagnetic half-metallic properties. Additionally, the Ga_1–xCr_xSb have good absorption ability in the infrared region, compatible with zinc-blende semiconductors such as GaSb, which makes Ga_1–xCr_xSb have promising potential applications in both spintronic devices and infrared optoelectronic devices.