The intensity distribution of focused spatial-variant polarized Bessel-Gauss vector beams is numerically simulated in the vicinity of the focal plane by using Richards-Wolf vectorial diffraction method. The existence of the focal shift in the negative direction of propagation is proved. The magnitude of the focal shift is closely associated with the order number of beam, beam width, wavelength and local polarization. The polarized state can be changed by adjusting the phase delay angle of the liquid crystal variable retarder, which can be continuously varied from 0 to π. The controllability of the focal shift in real time aroused by the phase delay angle will have great potential applications in optical micro-manipulations.