This paper presents a method for estimating the position and orientation of a camera with respect to a known 3-D object from line correspondences. The main idea of the method is to estimate a pose with either a weak perspective or a paraperspective camera model and to improve this pose iteratively. At convergence the result is compatible with a perspective camera model. This iterative improvement of a linear (affine) camera model has already been used for points but has never been extended to lines. Known methods which compute pose from line correspondences deal with a set of non-linear equations which are solved either in closed-form or using minimization techniques. These methods have to deal with multiple solutions. In contrast our method starts with a solution which is very close to the true solution and converges in very few iterations (typically 3 to 5 iterations). The rank analysis of the linear system to be solved at each iteration allows us to characterize geometric configurations which defeat the algorithm.