Abstract: The establishment and solution of a PnP problem are investigated here, and a vector difference based solution algorithm for linear P5P problem with an un-calibrated camera is proposed. Five control points are divided into collections containing four points of non-planar. According to the process of image formation, the constraint equations are set up between two collections of vector differences of control points. Then, these equations are simplified and determined in terms of linear theory and the orthogonal relation of rotation R. As a result, the analytic solutions of camera pose and intrinsic parameter matrix are obtained via vector cross or inner product operation. Simulated and real experiments illustrate that the proposed algorithm is effective.