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Motion-based 3D reconstruction (SfM) with missing data has been a challenging computer vision task since the late 90s. Under perspective camera model, one of the most difficult problems is camera auto-calibration which means determining the intrinsic camera parameters without using any known calibration object or assuming special properties of the scene. This paper presents a novel algorithm to perform camera auto-calibration from multiple images and dealing with the missing data problem. The method supposes semi-calibrated cameras (every intrinsic camera parameter except for the focal length is considered to be known) and constant focal length over all the images. The solution requires at least one image pair having at least eight common measured points. Tests verified that the algorithm is numerically stable and produces accurate results both on synthetic and real test sequences.