The Shack-Hartmann wavefront sensor (SHWS) generally requires that the focal spot of each microlens must remain in its corresponding sub-aperture area so that it is easy to decide the mapping relationship of spots and subapertures. We present a software-based recognition method, i.e., an iterative extrapolation method, which can still find the corresponding spot of each subaperture when the spots get out of their subaperture areas, so that the SHWS obtains a much larger dynamic range. First, this method finds a 3×3 sortable spot-array and establishes a polynomial function for the relationship between the centroid coordinate of the spot and its row and column numbers to predict and find the adjacent spots. Then it uses a new 3×3 spot-array on the edge of the already-found spots to continue searching outwards until all the spots are found. Finally, it decides the corresponding spot of each subaperture by adjusting all the row and column numbers by an offset. The performance of this iterative extrapolation method to expand the dynamic range of the SHWS under various types of wavefront aberrations is studied by simulation, and the experiments are carried out to further verify the practicability of this method.