In this paper, a novel three degrees of freedom (DoFs), that are two degrees of translational freedom and one degree of rotational freedom, parallel robot is proposed. The parallel robot consists of a base plate, a movable platform, and three connecting legs. Because the locus of any point on the moving platform is the subset of a cylinder if z is specified, the robot is called a cylindrical parallel robot. The inverse and forward kinematics problems are described in closed forms. And the velocity equation of the new parallel robot is given. Three kinds of singularities are presented. The workspace for the robot is analyzed systematically, especially, a new index to evaluate the mobility (In this paper, mobility means rotational capability.) of the moving platform of the robot is defined and discussed in detail. The parallel robot has wide application in the fields of industrial robots, simulators, microrobots and parallel machine tools.