The dynamic response of a power law based functionally graded (FG) rotor-bearing system with a slant crack has been analysed in the present work. The vibration response of an FG rotor-bearing system with a slant crack has been simulated using the Houbolt time marching scheme for different crack depths. The time-domain vibration responses are converted into the frequency domain using Fast Fourier Transform (FFT) to identify the crack features in order to detect and monitor the cracks. The sub-harmonic frequency components of the steady-state frequency spectrum were centred on the FG rotor’s operating speed, separated by the interval frequency corresponding to the torsional frequency. The sub-harmonic frequency components of the transient state frequency domain were found to be centred on the critical speed of the FG rotor system. The subharmonic frequency components of the dynamic response confirm the existence of a crack in the FG rotor system, which could be used to detect the crack in an FG rotor system.