The reflection and refraction of chirped Gaussian pulse at a moving step refractive-index boundary are investigated. When a chirped Gaussian pulse crosses a temporal boundary, the shape of the reflected spectra is distorted by adjusting chirp parameters. However, the transmitted spectra retain the Gaussian shape. The shape of the final output spectra is the same if the absolute values of the chirp are the same. By changing the chirp values, we can control the energy of the reflected and transmitted pulses, and the splitting distance of the pulse at the temporal boundary. By adjusting the time-dependent refractive index, chirped Gaussian pulses can experience total internal reflection at the temporal boundary. When pulse splitting occurs in an anomalous dispersion region, the velocity of the transmitted pulse decreases.