During the construction and long-term operation, stress concentration zones (SCZs) will inevitably occur in buried pipelines. It may cause pipe leakage or fracture failure. Therefore, it is essential to inspect the precise position and stress damage degree of SCZs. Pipeline non-contact magnetic-based stress inspection (PMSI) is an important issue in the oil and gas pipeline stress inspection field. In order to determine the response of the non-contact magnetic gradient signal on stress damage of SCZs, we established a pipeline magnetic-based stress detection model to analyse the three-dimensional magnetic signal of SCZs. The effect of changes to the axial stress value, the stress concentration length, the detection height, and the gradiometer jitter is also studied. Moreover, the PMSI is carried out on a 10.3 km LNG buried pipeline, which is validated by the excavation inspection results. The results indicate that the Gx shows sinusoidal fluctuation near the SCZ. The Gy and Gz reach a peak value. The Gmax increases with the severity and length of SCZs. Two level-II SCZs and two level-III SCZs are found.