Calculations of the direct radiative capture reactions are made for the $^{48}$Ca$(n,gamma)^{49}$Ca, $^7$Li$(n,gamma)^8$Li and $^{12}$C$(p,gamma)^{13}$N reactions with the Perey-Buck type nonlocal potentials using a potential model. Our results reproduce the experimental data reasonably well. From comparisons with results obtained by using local potentials, it is found that the cross sections of direct capture reactions may change by around 25% due to the nonlcality of nuclear potentials.