Based on the Fourier transform method, the analytical expression for the power spectrum of diffracted chirped Gaussian pulses in the far field is derived. Detailed numerical calculations are performed to illustrate the far-field spectral behavior and temporal intensity distributions of diffracted chirped Gaussian pulses. It is shown that the spectrum may be redshifted, blueshifted, and split into two or more than two parts, and the shifting of maximum and splitting of temporal intensity profiles occur. The far-field spectral behavior and temporal intensity distributions of ultrashort chirped Gaussian pulses diffracted at an aperture depend on the truncation parameter δ, pulse duration T, chirp parameter C and diffraction angle α. Specifically, for ultrashort chirped pulses there exists also the spectral switch.