The solar speckle image has the characteristics with single features, more noise, and blurred local details. Most of the existing deep learning deblurring methods for solar speckle images have some problems, such as high-frequency loss, artifact generation, and dependence on the paired image. In this paper, a deep prior deblurring method fusing the regularization model and prior constraint network is proposed. Firstly, the traditional handcrafted regularization priors are added to the network parameterized blind deconvolution model. The image gradient prior and blur kernel initial parameters are respectively used to the network parameterization process of two variables in the blind deconvolution model, which are the latent clean image variables and blur kernel variables. After that, the solar speckle image deep prior deblurring model is established. Secondly, the blur kernel generation network input is estimated by using the atmospheric point spread function (PSF) to improve the model convergence speed. Thirdly, a latent clean image generation network including joint gradient branching and Feature Pyramid Network (FPN) structure is designed to enhance image local edge details. Finally, a joint loss function including pixel loss, image prior loss, and mean squared error (MSE) loss is introduced to guide the model for alternate training. It can obtain the best parameter values of latent clean image and blur kernel, and achieve the solar speckle image high-resolution reconstruction. The experimental results show that the proposed method can eliminate the dependence on the reference image, and the reconstructed image has less noise and more obvious high-frequency details, faster network convergence, and two evaluation indicators of Peak Signal Noise Ratio (PSNR) and Structural Similarity (SSIM) are significantly improved.