Based on the nonparaxial vectorial moment theory of light beam propagation proposed by Porras, the characteristic parameters, such as the beam width, far-field divergence angle and M2 factor of nonparaxial vectorial Laguerre-Gaussian (LG) beams with initial circular polarization, are derived and expressed in terms of a series sum. The nonparaxial vectorial Gaussian beam is treated as a special case of our result. It is shown that the second-order-moment based beam width propagates according to the hyperbolic law, and for w0/λ→0 (w0-waist width,λ-wavelength) the far-field divergence angle θ approaches 90°, which is larger than 63.435° predicated by the nonparaxial scalar theory. The M2 factor of nonparaxial vectorial LG beams depends not only on the mode index p, but also on the w0/λ. Finally, comparison between the propagation of nonparaxial vectorial LG beams and that of nonparaxial scalar LG beams indicates that the far-field divergence angle is greatly influenced by the vectorial effect when w0/λ is relatively small. The problem which results from θ→90° and the applicability of the nonparaxial vectorial moment theory as well as the possible method for solving the problem are discussed.