Lucky imaging is able to reconstruct high-resolution images effectively from astronomical images affected by atmospheric turbulence. Its image reconstruction process can be carried out in the spatial domain or in the Fourier domain. This paper extend the lucky imaging technique to the wavelet domain, and proposes a lucky imaging method based on wavelet analysis. First, the short-exposure astronomical images are decomposed into four subbands by using the bior3.7 wavelet basis. Then, for the low-frequency subbands, the components with higher wavelet coefficients are extracted in a given selection ratio for fusion. For the high-frequency subbands in the horizontal, vertical, and diagonal directions, taking the whole subband as a unit, the subbands with smaller sums of wavelet coefficients are extracted for stacking in a given selection ratio. Finally, an inverse wavelet transform is performed on the four fused subbands to reconstruct the resultant image. Experimental results show that the proposed algorithm can better extract the details hidden in the original short-exposure astronomical images and obtain a higher-resolution image, and that it has a good image restoration effect.