The numerical simulation method was used to study the spectral characteristics of chirped Gaussian pulses constrained by Gaussian aperture in a dispersive medium. A model of chirped Gaussian pulses constrained by Gaussian aperture in a dispersive medium was established. The expression of the power spectrum was derived. Based on the power spectrum expression, the influence of factors such as the Gaussian aperture radius, chirped parameters, the distance of propagation , and off-axis radius on the spectral characteristics was simulated and analyzed. The results show that the influence of the chirped parameter on the spectrum depends only on its absolute value, the chirped parameter deviates the near-field spectrum from the Gaussian distribution, and the limitation of Gaussian aperture can effectively suppress this deviation. The larger the absolute value of the chirped parameter, the slower the spectrum in the far field is attenuated in the direction of propagation, the faster the attenuation in the off-axis direction, and the more concentrated the energy is on the optical axis. The spectrum attenuates faster in the direction of propagation with the limitation of Gaussian aperture than that without it, while slower in the off-axis direction, and the red-shift and the spectral width compression are significantly reduced in the off-axis direction. As the distance of propagation increases, the spectrum shifts blue on the axis and approaches the Gaussian distribution in the far field and the center frequency of the spectrum approaches a asymptotic value.