We have implemented a practical fast Fourier transform technique for fast and approximate calculation of terrain effects for airborne measurement of the gravity gradient tensor and the total magnetic field. The calculations proceed in two steps. Starting from a digital terrain model (DTM), we first calculate the fields on a plane surface lying above the highest point of the terrain in the selected area. This calculation can be made arbitrarily accurate by including a sufficiently large number of terms in Parker’s well-known Fourier transform technique. The second step involves a downward continuation of the fields to a draped surface describing the positions of the airborne measurements. The inherent instability of downward continuation through the level of the highest terrain is compensated for by low-pass filtering the calculated fields on the plane surface prior to downward continuation. We use a Gaussian filter with cutoff wavenumbers well below the Nyquist wavenumber corresponding to a wavelength equal to the distance between flight lines. Tests on synthetic data as well as on real data from a DTM from northern Sweden demonstrated that the method works well and provides a low-pass-filtered version of the true terrain effect.