In order to implement robot path planning according to the surgery optimum pose, the wrist dexterity of minimally invasive surgical robot was geometrically investigated. According to the structure and characteristic of minimally invasive surgical robot tools, wrist dexterity was analyzed by using analytic method of tool pose sphere. The impact of predefined pose of tools on the wrist dexterity was studied. It was proved that when the tool axes and the endjoint axes are perpendicular, 2-DOF wrist could meet the dexterity requirementsof minimally invasive surgery. The impact of axis setover of joints on wrist dexterity was studied. It was proved that when the setover along Z axis exists, the end tool could realize poses in all orientation. Based on these principles, the necessary conditions of how 2-DOF wrist becomes dexterous wrist were proposed. According to the conditions, the wrist structure of minimally invasive surgical robot is simplified.