The three-dimensional (3D) modeling and recognition of 3D objects have been traditionally performed using local features to represent the underlying 3D surface. Extraction of features requires cropping of several local surface patches around detected keypoints. Although an important step, the extraction and representation of such local patches adds to the computational complexity of the algorithms. This paper proposes a novel Keypoints-based Surface Representation (KSR) technique. The proposed technique has the following two characteristics: (1) It does not rely on the computation of features on a small surface patch cropped around a detected keypoint. Rather, it exploits the geometrical relationship between the detected 3D keypoints for local surface representation. (2) KSR is computationally efficient, requiring only seconds to process 3D models with over 50,000 points with a MATLAB implementation. Experimental results on the UWA and Stanford 3D models dataset suggest that it can accurately perform pairwise and multiview range image registration (3D modeling). KSR was also tested for 3D object recognition with occluded scenes. Recognition results on the UWA dataset show that the proposed technique outperforms existing methods including 3D-Tensor, VD-LSD, keypoint-depth based feature, spherical harmonics and spin image with a recognition rate of 95.9%. The proposed approach also achieves a recognition rate of 93.5% on the challenging Ca'Fascori dataset compared to 92.5% achieved by game-theoretic. The proposed method is computationally efficient compared to state-of-the-art local feature methods.