Time-frequency analysis (TFA) is widely used in the mechanical equipment fault diagnosis, but the current methods cannot deal well with multi-component signals, especially those with cross-frequency trajectories. This paper develops an iterative method for parameterized adaptive matching of generalized demodulation transform (PAMGD). It works by a series of angle parameters to calculate a time-frequency representation (TFR) of the signal, and utilizing the fusion of multiple indicators to guide the selection of angles at each moment point. The angles matched to the signal are retained for generating the final TFR. The signal mode with the highest amplitude in the signal is iteratively estimated and the residual signal is updated by removing the detected mode. PAMGD clearly shows TFR with multiple components and cross-frequency trajectories. The effectiveness of the proposed method in enhancing the TFR and handling cross-frequency trajectories is verified by simulation and experimental signals.