We demonstrate that the amplitude of vector-vortex beams has a Bessel-Gauss (BG) distribution through a rigorous vector electromagnetic analysis. We also investigate the intensity profiles in the focal plane of vector-vortex beams that are focused by a high numerical-aperture lens obeying the Helmholtz condition. Although the intensity of a vector-vortex BG beam with a topological charge n=1 is nonzero along the axis in the focal plane, the beams with n≠1 show discrete multiple spots which can be useful for optical trapping.