By using the vector Rayleigh diffraction integrals, an analytical expression for the diffraction of nonparaxial vector Gaussian beams at a circular screen is de rived. The diffracted on-axis field and farfield expressions and free-space pro pagation equation of nonparaxial vector Gaussian beams, as well as the paraxial Fresnel and Fraunhofer diffraction formulae of Gaussian beams diffracted at a ci rcular aperture are treated in a unified way as special cases of our general res ult. Numerical comparative examples are given to illustrate the intensity distri butions and far-field behavior of nonparaxial vector Gaussian beams. It is show n that for the diffraction at the circular screen both the f-parameter and truncation parameter affect the beam nonparaxiality.