In this paper, a linear approach is proposed to determine the camera’s intrinsic parameters as well as its pose. At first, the images of the two circular points are derived from the images of two unparallel coplanar rectangles in space, then some linear constraints on the intrinsic parameters are established via the obtained images of the circular points. In addition, the necessary and sufficient condition of the constraint system for a unique solution is also provided. Having obtained intrinsic parameters, the camera’s pose can be computed from the homography between the image plane and the space plane. Besides, a linear approach is also presented to retrieve the metric information (i.e., the Euclidean one up to a scale) of the rectangles by means of the Laguerre theorem. The main advantage of these approaches lie in that neither the metric information of the rectangles nor the correspondences between images are required, and the involved algorithms are all linear. Extensive simulations and experimental results with real images show that these proposed approaches are both accurate and robust.