A diffractive optical element is designed, and the element can be used to modulate the incident azimuthally polarized Laguerre-Gaussian vector beam. A three-dimensional multipoint optical trapping structure (twin-optical chain) is obtained along optical axis near the focal plane of high numerical aperture focusing lens. The effects of the parameters of incident beam (the topological charge and the radial mode number of associated Laguerre polynomial and the interception ratio of incident beam), the structures of inner and outer rings of the diffractive optical element, and the numerical aperture of the focusing lens on the twin-optical chain are analyzed. Results show that the structure of twin-optical chain is destroyed when we change the topological charge and the radial mode number, the twin-optical chain can be obtained again when we adjust the interception ratio and the structure of the diffractive optical element, and the high degree of freedom control of the twin-optical chain can be achieved.