Recently, self-calibration algorithms that use only the information in the image have been actively researched. But most algorithms require bundle adjustment in the projective reconstruction or in the nonlinear minimization. We propose a practical self-calibration algorithm that only requires a linear projective reconstruction. We overcome the sensitivity of the algorithm due to image noises by adding another constraint on the principal point. Also we propose a variant of linear auto-calibration algorithm which uses the similar assumption of the work of , based on the property of the absolute quadric. Experimental results using real and synthetic images demonstrate the feasibility of the proposed algorithm.