Lucky imaging is a post processing technique which can reconstruct a high resolution image for adaptive optics. In classic lucky imaging algorithm, only a few images which meet the image quality criterion are selected, shifted and added to reconstruct a final image, with image resolution reaching diffraction limited resolution of the large ground-based optical telescopes. However, high resolution information in given direction of the unselected images is rejected as a result. As to the lucky imaging in frequency domain algorithm, the information is selected in Fourier domain for every frame. It selects Fourier complex values with highest amplitude values at each spatial frequency below the cut-off frequency. Therefore, it makes a more efficient use of high resolution information contained in the short exposure images. Simulation results show that lucky imaging in frequency domain can overcome the effect of the atmosphere turbulence and improve the ability of the telescope. The results on real world astronomical images show that the lucky imaging in frequency domain often yields final image of better quality than classic lucky imaging algorithm at an equivalent selection ratio without an adaptive optics system.