In order to comprehensively analyze the effect of error factors on the magnetic gradient tensor, an integrated error model of the magnetic gradient tensor is established. It integrates five error factors, including three-axis non-orthogonal (TANO), three-axis sensitivity inconsistency (TASI), zero offset (ZO), coordinate system misalignment (CSM) and three-axis non-common point (TANCP). In addition, an iterative orthogonal experiment method is proposed to analyze the values of error caused by these factors and determine the calibration priority of all factors. The simulation result shows that the five error factors on the magnetic tensor from great to small is: TASI, TANO, CSM, ZO, TANCP. At the same time, the error factor which has a greater effect has a higher calibration priority level. When the circumstances occur, in which not all errors need be calibrated, error factors with higher priority should be calibrated first.