Based on fractional Schrödinger equation with variable coefficient, the transmission characteristics of symmetric Pearcey pulse are studied. When the variable coefficient is not considered, it is found that under the action of Lévy index, the symmetric Pearcey pulse splits into two pulses of equal intensity. Especially, when Lévy index equals one, the two Pearcey pulses can maintain the stable transmission over a long distance. When the variable coefficient is considered, under the action of periodic modulation, the symmetric pulse is periodically focused during transmission. The pulse is reshaped at the focal point and the intensity remains basically unchanged. Secondly, the influence of Lévy index and chirp parameter on the transmission characteristics of Pearcey pulse is discussed. The results show that the pulse intensity at the focal point can be controlled by Lévy index and the chirp parameter. The larger the Lévy index, the greater the intensity at the focus. Similarly, the larger the absolute value of the chirp, the greater the intensity at the focus. In addition, the influence of different parameters on the Pearcey pulse interaction is also studied. The change of the pulse spacing and phase, pulse intensity at the focus will also change accordingly.