The properties of off-center Gaussian vortex beams focused by a high numerical aperture are investigated on the basis of vector Debye integral. A complex amplitude of off-center Gaussian vortex beams through a high numerical aperture objective is derived and numerical calculation is performed to analyze the intensity and phase distributions of the beams in the focal plane. It is shown that the intensity and phase distributions change significantly with the variation of off-axial distance; the intensity distribution in the focal plane is different in the direction of y-axis which is enhanced with the increase of off-axial distances; the sign of off-axial distance determines the direction in which the intensity is concentrated. On the other hand, different from the 1st order off-axial vortex beam, high-order off-axial vortex will split in the tightly focused field. Multiple phase singularities will appear and the number of singularities is equal to the topological charge of the original beam. Besides, the split singularities are symmetric, obviously. It is found that the splitting of high-order vortex is due to the tight focusing.