The focusing property of concentric three-ring non-uniform mixing polarization vector beams through a high numerical aperture is theoretically investigated near the focal plane by using Richards-Wolf vectorial diffraction method. This kind of vector beams can be obtained by letting a concentric three-ring local linearly polarized cylindrical vector beam passes through a phase retarder with a phase angle δ. The three ring local linearly polarized cylindrical vector beam consists of the outer circle whose polarization is along the radially inward, the inner circle portion whose polarization is along the radially outward and the centray circle whose polarization direction has an angle φ2 with radial direction. The results of the numerical simulation show that the focusing intensity distribution of the non-uniform mixing polarization vector beams is closely related with parameters φ2 and δ. It is shown that the 3D dark optical chain along optical axis can be obtained near the focus by modulating the value of φ2 and δ, which has potential application in the optical micro-manipulation.