Abstract: In order to obtain the accurate output of the tensor measurement, an integrated mathematical model of sensor biases, scale factors and non-orthogonality error of single magnetic sensor and the misalignment error between multi-sensor axes is established. Based on the cross magnetic gradient tensor system, a least-squares nonlinear integrated calibration method is proposed. Compared with the twostep scalar calibration, the integrated mathematical model can be used to estimate the entire 48 error parameters of the cross tensor system at once, and a low-cost vector calibration is realized using an man-made platform out-put as the reference, which greatly improves the calibration efficiency and accuracy of parameters estimated. Simulation and experiment results show that the accuracy of the error parameters' estimation of the tensor system is higher than 99.75%, the root mean square error of the total field intensity output is less than 2 nT and the root mean square error of the tensor component is less than 50 nT/m.