Laue crystal monochromator are commonly used to monochromate high-energy X-rays (above 50 keV). Through bending the thin crystal, focused monochromatic beams could be obtained. However, twisted deformation would inevitably occur during bending crystal, which seriously affects monochromator efficiency. In this paper, wave optics simulation method was applied to study the influence of the bent crystal twisted on the performance of the Laue crystal monochromator. Moreover, in order to eliminate the crystal twist, a rotary mechanism of rotation angle fine adjustment was designed. The rotary mechanism includes a series of flexure hinges arranged symmetrically. Furthermore, the dynamics performances of the mechanism were also analyzed by using finite element method. The results show that when the rotation angle was within ±2°, the maximum shift of rotation center was less than 20 μm, the angular resolution achieved less than 1″ and dynamic range was up to 104,which totally meet the design requirements.