In standard digital color imaging, each pixel position acquires data for only one color plane and the remaining two color planes must be inferred through a process known as demosaicking. Furthermore, the image is susceptible to blurring artifacts due to a moving camera or fast moving subject. In this work we develop a robust framework to demosaick the color filter array (CFA) image while reducing the blur corrupting the image. We begin by defining a color motion blur model that describes the motion blur artifacts affecting color images. We then integrate the motion blur model in the demosaicking algorithm to obtain a computationally efficient framework for deblurring while demosaicking.