Weld surface defect recognition plays a vital role in the welding process and quality control. The classical two-dimensional principal component analysis (2DPCA) algorithm using the F norm metric in weld defect recognition suffers from the problems of being sensitive to abnormal deviation values and noise, poor robustness, and not being able to effectively reduce the reconstruction error while the projection distance is maximum. Aiming at the above problems, this paper uses a joint-norm metric, a two-dimensional principal component analysis algorithm called L1-2DPCA-R1 is proposed by adding L1 and R1 norm to the function model, and the iterative solution method of the algorithm is listed. This algorithm reduces the reconstruction error of the image, has better reconstruction performance, suppresses the influence of abnormal deviation values and noise, improves the robustness, and maintains the advantage of classification rate. Experiments show that the algorithm can accurately detect various weld defect types, with better resistance to large noise, better robustness, and smaller reconstruction error than other principal component analysis (PCA) algorithms.