In this paper, a new method for calculating effective atomic radii within the generalized Born (GB) model of implicit solvation is proposed, for use in computer simulations of bio-molecules. First, a new formulation for the GB radii is developed, in which smooth kernels are used to eliminate the divergence in volume integrals intrinsic in the model. Next, the Fast Fourier Transform (FFT) algorithm is applied to integrate smoothed functions, taking advantage of the rapid spectral decay provided by the smoothing. The total cost of the proposed algorithm scales as O(N(3)logN + M) where M is the number of atoms comprised in a molecule, and N is the number of FFT grid points in one dimension, which depends only on the geometry of the molecule and the spectral decay of the smooth kernel but not on M. To validate our algorithm, numerical tests are performed for three solute models: one spherical object for which exact solutions exist and two protein molecules of differing size. The tests show that our algorithm is able to reach the accuracy of other existing GB implementations, while offering much lower computational cost.