Industrial robots have advantages of large workspace, compact structure, and good flexibility, but the stiffness of the robot is relatively weak due to the compliance of reducers and its series structure. In this article, a five-degree-of-freedom robot with non-backlash driving is presented. A parallelogram structure with diagonal driven is used for robotic arms which is useful to improve the overall stiffness of the robot. First, the detailed structure of the robot is introduced, and the kinematic characteristics of the robot are analyzed. Second, a stiffness approximation method is proposed to evaluate the stiffness of the robot in the global workspace. The overall deformations under certain external loads which are composed of deflection deformations and stretching deformations are calculated based on the strain energy method and the properties of the components. The effectiveness of the approximation method used for evaluating the stiffness of the robot which has hybrid open-and closed-loop kinematic chains is verified through the finite element analysis results and the experimental results. Finally, the stiffness evaluation results show that the stiffness of the proposed robot is better than that of the industrial robot, which makes it more suitable for most of the industrial applications, such as handling, palletizing, and drilling.