The invention relates to an asymmetrical completely-isotropic three-degree-of-freedom parallel connection robot mechanism which comprises a movable platform, a fixed platform, and three different branch kinematic links for connecting the movable platform with the fixed platform, wherein the first branch kinematic link comprises a first cylindrical pair, a first rotating pair, a second rotating pair and a third rotating pair, rotating axial lines of the first rotating pair and the second rotating pair are parallel with the axial line of the first cylindrical pair and vertical to the rotating axial line of the third rotating pair; the second branch kinematic link comprises a first movable pair, a second movable pair and a fourth rotating pair, the axial line of the first movable line is vertical to the axial line of the second movable line and parallel with the rotating axial line of the fourth rotating pair; and the third branch kinematic link comprises a fifth rotating pair, a first hook joint, a third movable pair and a second hook joint, and the axial line of the first movable pair is vertical to the rotating axial line of the first cylindrical pair and parallel with the axial line of the fifth cylindrical pair. By using the mechanism in the invention, the problems of poor kinematics decoupling property and poor rotating property of the traditional robot mechanism can be solved.