Based on a single-channel laser self-mixing interferometer, we present a new simultaneous measurement of the vibration amplitude and the rotation angle of objects that both affect the power spectrum containing two peaks of the interferometer signals. The fitted results indicate that the curve of the peak frequency versus the vibration amplitude follows a linear distribution, and the curve of the difference of the two-peak power values versus the angle follows a Gaussian distribution. A vibration amplitude with an error less than 3.0% and a rotation angle with an error less than 11.7% are calculated from the fitted results.