The mechanical vibration source signals with common frequency components cannot satisfy a statistically independent condition and be directly separated by a traditional blind source separation method. In order to solve this problem, a novel correlated source separation method based on modified S-transform (MST) and independent component analysis (ICA) is proposed. First of all, the modified S-transform is used to the time-frequency preprocessing of observation signals, taking advantage of the vector angle of the components in the real and imaginary parts of the time-frequency domain, and identifying and eliminating the dependent components in the mixed signals to ensure that the new reconstruction signals satisfy the independence condition. Then, using the negative entropy as an independent measure, the separation matrix is estimated based on the fast fixed-point independent components analysis. Finally, the correlated source signals are recovered through the matrix separating the initial observation signals and quantitatively calculated the contribution ratio of each vibration source. The effectiveness of proposed method in correlated source separation is verified by simulation and experiment results.