In this paper, we present a generalized Peierls-Nabarro model for curved dislocations using the discrete Fourier transform. In our model, the total energy is expressed in terms of the disregistry at the discrete lattice sites on the slip plane, and the elastic energy is obtained efficiently within the continuum framework using the discrete Fourier transform. Our model directly incorporates into the total energy both the Peierls energy for the motion of straight dislocations and the second Peierls energy for kink migration. The discreteness in both the elastic energy and the misfit energy, the full long-range elastic interaction for curved dislocations, and the changes of core and kink profiles with respect to the location of the dislocation or the kink are all included in our model. The model is presented for crystals with simple cubic lattice. Simulation results on the dislocation structure, Peierls energies and Peierls stresses of both straight and kinked dislocations are reported. These results qualitatively agree with those from experiments and atomistic simulations.