Aiming at the key point description and repeatability in the method of key point detection of three-dimensional (3D) point cloud is not strong, and the number of detected key points is small, we propose a novel algorithm of key point detection. Firstly, in order to improve the efficiency of the algorithm, the uniform sampling method is used to reduce the number of points in the 3D point cloud that can reduce the complexity of the 3D point cloud. Then, we use Signature of Histograms of OrienTations (SHOT) descriptor to describe the points uniformly sampled in multi-scale, and analyze the uniqueness of the multi-scale SHOT descriptors at each point, and select the SHOT descriptor with larger discreteness of points as the key points. The proposed method uses the descriptive SHOT descriptor to describe the neighborhood of the key points, and enhances the descriptivity of the key points. The experimental results show that the uniform sampling is highly efficient in time and meets the time requirements of the keypoint detection. The proposed method has better reproducibility than Harris 3D, scale invariant feature transform (SIFT) and internal shape signature (ISS) key point detection algorithms in the key point detection. Therefore, the proposed method can detect high quality key points in the 3D point cloud model and scene effectively and quickly.