The invention discloses a two-freedom-degree rotation parallel mechanism. The parallel mechanism comprises a movable platform, a fixed platform, two driving branch chains and a suitable constraint branch chain, the two driving branch chains have the same structural form, and each driving branch chain is composed of a parallelogram structure, rotation pairs and ball pairs. The suitable restraint branch chain is formed by connecting a first rotating pair and a second rotating pair in series, wherein the axes of the first rotating pair and the second rotating pair are perpendicular. The third ball pair of the first driving branch chain is connected with a restraining connecting rod of the suitable restraint branch chain, and the sixth ball pair in the second driving branch chain is connected with the movable platform. The speed jacobian matrix of the parallel mechanism is a diagonal matrix, and in other words, one output motion of the movable platform is only controlled by the input motion of one driving pair, and the defect that the kinematics and dynamics coupling performance of a common parallel mechanism is high is overcome; and meanwhile, by introducing the suitable constraint branch chain, the overall stability and the bearing capacity of the parallel mechanism can be enhanced, the precision of the parallel mechanism can be improved, and uncontrollable errors can be controlled.