The finite element model (FEM) of an overhung rotor-bearing system is established. Oil-film instability features and the effect of angular accelerations on oil-film instability laws are analyzed during run-up and run-down processes by the time-domain waveform, spectrum cascade and amplitude-frequency response. The results show that the onset of oil-film instability changes due to the tangential inertia force from run-up and run-down processes, and the instability speeds under the run-up and run-down conditions will be delayed compared with that under stable conditions (with no angular acceleration). Moreover, the second mode instability speed increases slightly as angular acceleration increases in run-up conditions, and decreases slightly in run-down conditions. The phenomenon of hysteresis under run-down conditions can be observed compared with the run-up condition.