By solving the Schrödinger equation in spatial and temporal coordinates, the exact solution of the chirped Airy-Gaussian (CAiG) wave packets in a gradient-index medium is obtained. Based on that, we conduct a theoretical analysis about the properties of CAiG wave packets and discover that the chirp factor, the distribution factor, the initial velocity, as well as the propagation distance have an effect on the wave packets in both the propagation process and the spatiotemporal profiles. Among these, the Gaussian distribution factor, which is first added to the initial pulses, also alters the peculiarities of the Airy-Gaussian beams in the temporal domain and spatial domain. In addition, the investigation about the radiation force illuminates certain evolution properties of the CAiG wave packets well.