The structure of a novel 5-DOF industrial manipulator was analyzed. The homogeneous transformation matrix of the manipulator was obtained by establishing a series of D-H frames. Based on Paul’s inverse transformation, an analytical method that could direct the solution of inverse kinematics problems of series manipulators was proposed, and the closed-form solution of inverse kinematics was derived. Computational simulation results indicated that the algorithm was efficient and real-time. The enveloping surface of the local joints’ workspace was specified using envelop theory. Working dexterity of the manipulator was discussed. The dexterous workspace of the manipulator on which the structure design and motion control were based was established via geometrically overlaying the enveloping surfaces of local joints’ workspace.