To address the limitations of the scale invariant feature transform (SIFT) algorithm and reduce the computational burden of the Ane-SIFT (ASIFT) algorithm in scenes with large affine deformations, a fast image matching algorithm based on approximate-ane-SIFT (Fast-AASIFT) is proposed. Fast-AASIFT has a clearer physical meaning than the ASIFT algorithm. First, Fast-AASIFT recovers original images as rectified images by performing inverse affine transformations. Then, it performs feature point extraction and SIFT description on the rectified images. Finally, it performs SIFT optimization matching. The experimental results demonstrate that, in scenes with a large affine deformation, Fast-AASIFT can still match enough feature points, with a peak matching error of <2.5 pixels and an average matching error of <1.2 pixels. This proves that the anti-affine deformation ability of Fast-AASIFT is equivalent to that of the ASIFT algorithm, which is significantly better than that of the SIFT algorithm. Furthermore, the time consumed by Fast-AASIFT less than 30% of that consumed by the ASIFT algorithm; thus, it effectively addresses the time-consumption problem of the ASIFT algorithm. Obviously, Fast-AASIFT not only maintains good robustness against affine deformations but also greatly improves computational efficiency; consequently, it is of great value for applications such as scene reconstruction and recognition.