Based on the nonparaxial vectorial moment theory of light beam propagation, the propagation of TE (transverse electric) vector Gaussian beam has been investigated, and the integral expressions of beam waist, transversal divergence angle and beam propagation factor have been presented. The results reveal that both the transversal beam widths defined as second order moment of energy flux follow a very simple hyperbolic law upon propagation. The numerical calculations show that TE polarization results in different propagating characteristic in the two transversal directions for highly nonparaxial case, and the maximum transverse divergences exceed the divergence angle limit of nonparaxial scalar Gaussian beam 63.43° and are close to 90°, which is in accordant with the theory of wave optics. Moreover, the divergence in the x direction is slightly larger than that in the y direction. Under paraxial condition of nonparaxial scalar Gaussian beam, the propagation of TE vector Gaussian beam is reduced to that of transversal fundamental mode paraxial scalar Gaussian beam for paraxial case. However, the beam propagation factor will always be greater than unity and cannot accurately equal to unity forever.