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Object recognition and grasping plays a key role in robotic systems, especially for the autonomous robots to implement object sorting tasks in a warehouse. In this paper, we present a global texture-shape 3D feature descriptor which can be utilized in a system of object recognition and grasping, and can perform object sorting tasks well. Our proposed descriptor stems from the clustered viewpoint feature histogram (CVFH), which relies on the geometrical information of the whole 3D object surface only, and can not perform well in recognizing the objects with similar geometrical information. Therefore, we extend the CVFH descriptor with texture and color information to generate a new global 3D feature descriptor. The proposed descriptor is evaluated in tasks of recognizing and classifying 3D objects by applying multi-class support vector machines (SVM) in both public 3D image dataset and real scenes. The results of evaluation show that the proposed descriptor achieves a significant better performance for object recognition compared with the original CVFH. Then, the proposed descriptor is applied in our object recognition and grasping system, showing that the proposed descriptor helps the system implement the object recognition, object grasping and object sorting tasks well.