Abstract: Strong atmospheric turbulence reduces astronomical seeing, causing speckle images acquired by ground-based solar telescopes to become blurred and distorted. Severe distortion in speckle images impedes image phase deviation in the speckle masking reconstruction method, leading to the appearance of spurious imaging artifacts. Relying only on linear image degradation principles to reconstruct solar images is insufficient. To solve this problem, we propose the multiframe blind deconvolution combined with non-rigid alignment (MFBD-CNRA) method for solar image reconstruction. We consider image distortion caused by atmospheric turbulence and use non-rigid alignment to correct pixel-level distortion, thereby achieving nonlinear constraints to complement image intensity changes. After creating the corrected speckle image, we use the linear method to solve the wavefront phase, obtaining the target image. We verify the effectiveness of our method results, compared with others, using solar observation data from the 1 m new vacuum solar telescope (NVST). This new method successfully reconstructs high-resolution images of solar observations with a Fried parameter r₀ of approximately 10 cm, and enhances images at high frequency. When r₀ is approximately 5 cm, the new method is even more effective. It reconstructs the edges of solar graining and sunspots, and is greatly enhanced at mid and high frequency compared with other methods. Comparisons confirm the effectiveness of this method, with respect to both nonlinear and linear constraints in solar image reconstruction. This provides a suitable solution for image reconstruction in ground-based solar observations under strong atmospheric turbulence.