The problem of recognizing and locating rigid objects in 3-D space is important for applications in welding automation. This issue relates to finding a transformation matrix between the intended and actual locations to compensate for fixturing errors before welding starts. An algorithm of 3-D position estimation using a laser vision sensor is introduced for automatic die remodeling. First, a vision sensor based on optical triangulation was used to collect the range data on die surfaces for automatic remodeling. Second, line and plane vector equations were constructed from the measured range data, and an analytic algorithm was proposed for recognizing the die location with these vector equations. This algorithm produces the transformation matrix with no specific feature points. To evaluate the proposed algorithm, a corrugated SUS plate was measured with a laser vision sensor attached to a three-axis Cartesian manipulator, and the transformation matrix was calculated.