Direct band gap semiconductor gallium antimonide (GaSb) has applications in fiber optic communication and optoelectronic devices because of its excellent performance. In order to explore the potential applications of GaSb in optoelectronic devices and new spintronics materials, the electrical, magnetic and optical properties of GaSb at different Ti doping concentrations (denoted as Ga1-xTixSb, where X is the atomic percentage concentration of Ti) were calculated by first-principles. The calculated results show that the energy band structure and the density of states of Ga1-xTixSb generate spin splitting near the Fermi level and form a net magnetic moment, making the Ga1-xTixSb (x=0.25, 0.5, 0.75) show half-metal ferromagnet, dilute magnetic semiconductor and magnetic metallic, respectively. The lattice constant of Ga1-xTixSb increases after optimization. The refractive index, reflectivity and absorption coefficient of Ga1-xTixSb are red-shifted and have a higher optical absorption coefficient than that of undoped GaSb in the middle and far infrared band. The absorption of Ga1-xTixSb become better in the middle and far infrared band as the Ti doping concentration increases. The calculation results provide a theoretical reference for the expansion of GaSb-based semiconductor materials for applications in infrared detectors, infrared semiconductor lasers and the discovery of new materials for spintronics.