On the basis of vector Rayleigh diffraction integral formula,an analytical expression for the diffraction of nonparaxial vectorial off-axis elliptical Gaussian beam at a rectangular aperture is derived. And according to that,the on-off and far-field expressions for rectangular diffraction,the propagation formula in free space,slit diffraction and the paraxial far-field diffraction formulae are obtained. It is shown that the f parameter,truncation parameter and relative off-axis parameter affect together the beam nonparaxiality.