A 3D point cloud object recognition algorithm was studied based on the local descriptor. The information of vector and shape index value of the point cloud were calculated, and then according to the shape index, feature points were extracted. Based on the Euclidean distance and vector angle, points cloud were segmented into different patches centered on feature points. From the Equidistant partition on each patch, 3D European-style concentric circles were obtained. The vector angle and geodesic distance variation on the sample points of each circle were important information, so the description of three-dimensional objects could be transformed into two two-dimensional curves, the normal vector curves and the geodesic distance curves. One model objects database would be established firstly. Through comparison of the descriptions of tested object with the model database, some potential recognition results could be found. With the finally iterative closest point algorithm, the final recognition result would be obtained. Experimental results with real objects, and time consuming comparison with other algorithms were presented to demonstrate the effectiveness of the proposed algorithm.