Effects of finite-range tensor force on β-decay of magic and semimagic nuclei of 34Si,68,78Ni,and 132Sn have been investigated using the self-consistent Hartree-Fock plus random-phase approximation model.The ten-sor force shifts the low-lying Gamow-Teller states downward and systematically improves the calculations of Q and log ft values.Consequently,it systematically reduces the deviations between the theoretical and experimental data and significantly improves the calcu-lation of β-decay half-lives.This effect is similar to that of zero-range tensor force.