We regard the gridding of aeromagnetic data as a geophysical estimation problem and propose to use the inverse interpolation method for gridding aeromagnetic data. The gridding method we present is based on Tikhonov's regularization theory by setting up the data fitting goal and the model smoothing goal. The interpolation operator in the data fitting goal is chosen to be a Gaussian weighted operator. The smoothing filter in the model smoothing goal is chosen to be a Laplacian operator. The gridding equation is iteratively solved by using the preconditioning conjugate gradient algorithm, the preconditioning operator, which is the inverse of the Laplacian operator. The helix transform technique and Wilson's spectral factorization algorithm are used to make the filtering and inverse filtering of the Laplacian operator fast and stable. Gridding experiments were conducted on synthetic total field magnetic anomaly and real aeromagnetic data from a survey in South China and show that the method produced smooth and accurate results without obvious aliasing artefacts.