Affine reconstruction is to restore the affine shape of the object. Generally, there are two ways of achieving, one is to determine the plane at infinity, another is to determine the plane homography. Using the homography which had determined the plane at infinity achieve affine reconstruction. In this paper, firstly give out the homography of infinity plane and the algorithm of affine reconstruction, then proved: if the scene contains a set of parallel planes and a infinity point, the homography of infinity plane can be obtained and affine reconstruction can be linearly got in the scene. Computer simulation and real experiments show that the linear affine reconstruction algorithm is correct, and the approach has a good precision.