In classic matrix differential multiple-input multiple-output random vibration control algorithm,matrix decomposition and matrix differentiation operation is needed,which is complicated in calculation and is not conducive to real-time applications.Aiming at a kind of multi-axis random vibration tests with low coherence coefficient,Newton method was used to derive the excitation spectrum iterative equation,and an iterative correction algorithm was proposed for the drive spectrum,by which the control calculation was simplified and the real-time performance was improved.The algorithms convergence and the gain factor were theoretically analyzed.Numerical simulation was done to verify the algorithm.Finally,the three-axis vibration test was carried out.The results show that good control accuracy has been achieved in the power spectrum control test,which meets the needs of engineering applications.