Based on the variable coefficient nonlinear Schr?dinger equation, this paper investigates the dynamic characteristics of the symmetric Airy pulses with an initial chirp under periodic dispersion modulation. The results show that the chirp parameter C and the main lobe position d determine the number and positions of focal points generated by the collision during the transmission of the chirped symmetric Airy pulses. Within the evolution distance of a dispersion cycle, when |C|<0.5, one or two focal points can be generated by adjusting the position d of the main lobe as the pulse trajectory does not reverse. When |C|=0.5, the trajectory of the pulse will be reversed once, and there will be two focal points in the evolution of the pulse. The main lobe position d can only affect the position of the focal point; it does not affect the number of focal points. Furthermore, when |C|>0.5, the trajectory of the pulse will be reversed twice, and there are at least two focal points. Moreover, the number of focal points can be increased to three at most four by adjusting the main lobe position d. Additionally, the truncation parameter does not affect the number and the position of the focal points. However, a larger truncation parameter will lose more energy under collision. When the Kerr nonlinear effect is considered, the transmission characteristics of the pulse are nearly unchanged under the small nonlinear effect. As the nonlinearity further increases, it causes soliton shedding. Stronger nonlinear effect can also lead to the generation of multiple solitons and the collision of solitons with side lobes. This periodic transmission process and focusing characteristics provide certain theoretical guidance for the research and the application of properties, such as the self-reconstruction of Airy pulses.