Based on the Rayleigh-Sommerfeld diffraction integral,the far-field expression for ultrashort pulsed Gaussian beams with constant waist width in a linear dispersive medium is derived without involving the paraxial approximation,and used to study their far-field properties. The expression is applicable to the large diffraction angle. It is found that there exists a critical diffraction angle θ_c,for the power spectrum of pulsed Gaussian beams with constant waist width. The spectrum is blue-shifted if θ<θ_c,whereas,for θ>θ_c,the spectrum is red-shifted,and the redshift increases with increasing θ. Additionally,there is a time shift,which increases with an increase of θ,and the Gaussian pulse form can not remain unchanged in the far field. Finally,the group velocity dispersion results in the chirp,which increases with decreasing diffraction angle.