A geometric modeling method for the cross-sectional profile of welds in the tailored blank laser welding is proposed. The edges of the cross-sectional profile are extracted based on the Laws texture filtering and the mathematical morphological closed operation. The curve fitting for these edges of the cross-sectional profile are done with the polynomial function model, the exponential function model and the Gaussian function model, respectively. The error analysis of the fitting results is also conducted. The analysis results show that the fitting precision for the upper edge of the cross-sectional profile of welds based on the exponential function model is the highest, however the fitting precision for the lower edge of the cross-sectional profile of welds based on the Gaussian function model is the highest. The geometric modeling experiments for the edges of the cross-sectional profile of welds in the tailored blank laser welding under different welding parameters are carried out and the experimental results demonstrate that the proposed method is effective to realize the geometric modeling for the cross-sectional profile of welds in the tailored blank laser welding.