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Color image demosaicking aims to reconstruct the full-resolution RGB image from a mosaicked Color Filter Array (CFA) image. Instead of reconstructing the red, green, and blue color channels separately, most demosaicking approaches mutually recover them. However, CFA images tend to be distorted by the non-ideal response of the camera sensor, and possible motion or out-of-focus blurs during the acquisition. Demosaicking followed by deblurring is sub-optimal because demosaicking errors will be propagated into deblurring and amplified by the latter. This paper presents a regularization approach to jointly deblur and demosaic CFA images. By embedding a non-linear demosaicking algorithm into a regularized restoration method, the full-color RGB image can be recovered and refined iteratively. The numerical and visual results show that our approach is superior to other methods.