The development of nonstationary signal blind separation, especially an underdetermined mixture of nonstationary sources, has become increasingly important for mechanical multi-fault diagnosis. In this paper, a novel algorithm based on the adaptive parametric time-frequency analysis theory to blindly separate the mixtures of nonstationary sources is presented. The computer simulations illustrate the applicability of our approach, and the performance of the algorithm is successfully tested on the underdetermined blind source separation of five vibration signals of a high speed train from one instantaneous mixture of these signals.