A series of short-exposure images are often used for rich, small-scale structure, high-quality, and high-resolution astronomical observations. Postprocessing of the closed-loop adaptive optics (AO) image using ground-based astronomical telescopes plays an important role in astronomical observations due to it further improving image quality after AO processing. These images show several main characteristics: random spatial variation blur kernel, unclear model after AO correction, unclear physical characteristics of observation objects, etc. Our goal is to propose a multiframe correction blind deconvolution (MFCBD) algorithm to restore AO closed-loop solar images. MFCBD introduces a denoiser and corrector to help estimate the intermediate latent image and proposes using an L q norm of the kernel as the sparse constraint to acquire a compact blur kernel. MFCBD also uses the half-quadratic splitting strategy to optimize the objective function, which makes the algorithm not only simple to solve, but also easy to adapt to different fidelity terms and prior terms. In tests on three data sets observed from the photosphere and chromosphere of the Sun, MFCBD not only restored clearer and more detailed images, but also converged smoothly and monotonically in terms of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) after a few iterations. Taking the speckle-reconstructed image as a reference, the clear image restored by our method performs best both in PSNR and SSIM compared with the state-of-the-art traditional methods OBD and BATUD.