In automatic welding, multi-line laser structured-light vision sensors provide more adequate information to compared with traditional single-line structured light and are gradually being widely designed. However, when calibrating the sensor, a global calibration approach should be adopted in order that the laser intrinsic parameters follow the inherent constraints. In this paper, a Lagrange solution is shown and its unsuitability for general cases is qualitatively analyzed. We then propose a novel hierarchical iterative hypothesis (HIH) strategy to deal with issues with the following conditions. First, the configuration and pose (including rotation and translation) of a 3D model need to be solved. Second, the model can be obtained by scaling a known model in several dimensions. Third, part of sampling points of the model can be acquired. The proposed hypothesis is introduced based on the coordinate transformation theory. Hierarchical iteration, including global and local iteration, is elaborated mathematically, which utilizes singular value decomposition (SVD) and gradient descent technology. The process of applying hierarchical iterative hypothesis strategy HIH is illustrated, and a reconfirmation for transformation is introduced. The steps in the intrinsic parameters calibration for weld vision sensor are described. A calibration experiment is witnessed that the ambiguity on the intersection issue is reduced to compared with ordinary least square method for structured light calibration. Several quality measures were introduced that allow us to judge the performance of our method. Two experiments for verifying calibration results reveal that the proposed strategy earns a great calibration performance that can meet weld seam tracking needs.