Context. Due to the presence of atmospheric turbulence, the quality of solar images tends to be significantly degraded when observed by ground-based telescopes. The adaptive optics (AO) system can achieve partial correction but stops short of reaching the diffraction limit. In order to further improve the imaging quality, post-processing for AO closed-loop images is still necessary. Methods based on deep learning (DL) have been proposed for AO image reconstruction, but the most of them are based on the assumption that the point spread function (PSF) is spatially invariant. Aims. Our goal is to construct clear solar images by using a sophisticated spatially variant end-to-end blind restoration network. Methods. The proposed channel sharing spatio-temporal network (CSSTN) consists of three sub-networks: a feature extraction network (FEN), channel sharing spatio-temporal filter adaptive network (CSSTFAN), and a reconstruction network (RN). First, CSST-FAN generates two filters adaptively according to features generated from three inputs. Then these filters are delivered to the proposed channel sharing filter adaptive convolutional (CSFAC) layer in CSSTFAN to convolve with the previous or current step features. Finally, the convolved features are concatenated as input of RN to restore a clear image. Ultimately, CSSTN and the other three supervised DL methods are trained on the binding real 705nm photospheric and 656nm chromospheric AO correction images as well as the corresponding speckle reconstructed images. Results. The results of CSSTN, the three DL methods, and one classic blind deconvolution method evaluated on four test sets are shown. The imaging condition of the first photospheric and second chromospheric set is the same as training set, except for the different time given in the same hour. The imaging condition of the third chromospheric and fourth photospheric set is the same as the first and second, except for the Sun region and time. Our method restores clearer images and performs best in both the peak signal-to-noise ratio (PSNR) and contrast among these methods.