In this paper, a novel three-degrees-of-freedom (3-DOF) parallel robot is designed, which can only move in three translational directions. It avoids the difficulty in the solution for forward kinematics of the parallel robot. The robot containing only lower pairs (P and R) has a simple mechanism. The characteristic that the parallel robot has only three translational degrees of freedom can be proved by the screw theory and the DOF can be got by the formula of calculating the DOF of space mechanism. The kinematics and workspace of the parallel robot is analyzed through calculation and simulation. In order to obtain better servo control performance, the PMSM fuzzy controller is designed. The analysis and simulation results show that the mechanism design of the parallel robot is reasonable, and the effect of fuzzy controller is better than the ordinary PID controller.