Abstract: The areas of airborne gravity measurement are often irregular and the gravitational measurement data often have vacancy and high frequency noise interference. Conventional airborne gravity data processing generally performs the two steps of interpolation and denoising independently. In this paper, we consider these two problems in a unified way. Learning from seismic data processing methods, we propose an iterative method for interpolation and denoising of airborne gravity data based on the projection onto convex sets method. Using the simulative airborne gravity data based on the EGM2008, the results of numerical calculation examples have clearly demonstrated that our proposed iterative method for interpolation and denoising of gravity data is better than the four classical interpolation methods and some wavelet threshold denoising methods. And the effectiveness of the method is further verified by the measured aerial gravity data of a certain area.