The signal collected from grinding machines is a kind of compound signal mixed with several vibration sources. In order to isolate it, blind source separation (BSS) algorithm is used to improve the accuracy of condition monitoring and fault diagnosis. It is a common way to use fixed point iteration method based on kurtosis which has the problem of low convergence rate and unsteady isolation accuracy. To solve the problem, this paper proposed a new BSS method to maximize kurtosis based on Newton iteration. Through the simulated experiment, the number of iteration steps of this paper is 1/5000 that of fixed point method with better accuracy. Through the actual experiment of grinding machine, this algorithm gets the same operating parameters as the calculation, which further demonstrates this method can be better applied in practical engineering.