The influences of Lévy index, chirp parameter and potential depth on the propagation dynamics of chirped Gaussian beam are investigated numerically based on the fractional Schrdinger equation with a harmonic potential. It is found that, for fixed chirp parameter and potential depth, the propagation period decreases and the deviation distance increases with increasing of Lévy index. For fixed Lévy index and potential depth, the propagation period and the deviation distance increase as the chirp parameter increases. The period and the deviation distance are inversely proportional to the potential coefficient regardless of the values of Lévy index and chirp parameter. The results indicate that the beam propagation can be effectively controlled by adjusting Lévy index, chirp parameter and potential depth, which can inspire new ideas in the manufacture of optical switches.