A major advantage of wavefront reconstruction based on a series of diffracted intensity images using only single-beam illumination is the simplicity of setup. Here we propose a fast-converging algorithm for wavefront calculation using single-beam illumination. The captured intensity images are resampled to a series of intensity images, ranging from highest to lowest resampling; each resampled image has half the number of pixels as the previous one. Phase calculation at a lower resolution is used as the initial solution phase at a higher resolution. This corresponds to separately calculating the phase for the lower- and higher-frequency components. Iterations on the low-frequency components do not need to be performed on the higher-frequency components, thus making the convergence of the phase retrieval faster than with the conventional method. The principle is verified by both simulation and optical experiments.