Positron annihilation lifetime spectroscopy and Doppler broadening annihilation line-shape measurements were carried out in 40 MeV alpha-irradiated undoped InSb. After irradiation the sample was subjected to an isochronal annealing over temperature region of 25°C–400°C with annealing time of 30 min at each set temperature. After each annealing the positron measurements were carried out at room temperature. Formation of radiation induced defects and their recovery with annealing temperature were investigated. A three component positron lifetime analysis was undertaken to observe the trapping of positrons in the sample after irradiation and during annealing. The average positron lifetime value τ avg = 313 ps at room temperature after irradiation indicated the presence of defects and the high value of τ2 at room temperature suggested that the probable defects were divacancies. A two stage recovery of defects was observed during post irradiation isochronal annealing over the temperature region 25°C–400°C. The variations in line-shape parameter (S) and defect specific parameter (R) during annealing in the temperature region 25°C–400°C resembled the behavior of τ avg indicating the migration of vacancies, formation of vacancy clusters and the disappearance of defects between 300°C to 400°C.