Suppressing the interference of atmospheric turbulence and obtaining observation data with a high spatial resolution are an issue to be solved urgently for ground observations. One way to solve this problem is to perform a statistical reconstruction of short-exposure speckle images. Combining the rapidity of Shift-Add and the accuracy of speckle masking, this paper proposes a novel reconstruction algorithm-NASIR (Non-rigid Alignment based Solar Image Reconstruction). NASIR reconstructs the phase of the object image at each frequency by building a computational model between geometric distortion and intensity distribution and reconstructs the modulus of the object image on the aligned speckle images by speckle interferometry. We analyzed the performance of NASIR by using the correlation coefficient, power spectrum, and coefficient of variation of intensity profile in processing data obtained by the NVST (1 m New Vacuum Solar Telescope). The reconstruction experiments and analysis results show that the quality of images reconstructed by NASIR is close to speckle masking when the seeing is good, while NASIR has excellent robustness when the seeing condition becomes worse. Furthermore, NASIR reconstructs the entire field of view in parallel in one go, without phase recursion and block-by-block reconstruction, so its computation time is less than half that of speckle masking. Therefore, we consider NASIR is a robust and high-quality fast reconstruction method that can serve as an effective tool for data filtering and quick look.