We develop a new computational method for modeling and inverting frequency domain airborne electromagnetic (EM) data. Our method is based on the contraction integral equation method for forward EM modeling and on inversion using the localized quasi-linear (LQL) approximation followed by the rigorous inversion, if necessary. The LQL inversion serves to provide a fast image of the target. These results are checked by a rigorous update of the domain electric field, allowing a more accurate calculation of the predicted data. If the accuracy is poorer than desired, rigorous inversion follows, using the resulting conductivity distribution and electric field from LQL as a starting model. The rigorous inversion iteratively solves the field and domain equations, converting the non-linear inversion into a series of linear inversions. We test this method on synthetic and field data. The results of the inversion are very encouraging with respect to both the speed and the accuracy of the algorithm, showing this is a useful tool for airborne EM interpretation.