Recognizing three-dimensional (3D) objects based on local feature descriptors is a highly challenging task. Existing 3D local feature descriptors rely on single-scale surface normals, which are susceptible to noise and outliers, significantly compromising their effectiveness and robustness. A multi-scale point pair normal encoding (M-POE) method for 3D object recognition is proposed. First, we introduce the M-POE descriptor, which encodes voxelized features with multi-scale normals to describe local surfaces, exhibiting strong distinctiveness and robustness against various interferences. Second, we present guided sample consensus in second-order graphs (GSAC-SOG), an extension of RANSAC that incorporates geometric constraints and reduces sampling randomness, enabling accurate estimation of the object’s six-degree-of-freedom (6-DOF) pose. Finally, a 3D object recognition method based on the M-POE descriptor is proposed. The proposed method is evaluated on five standard datasets with state-of-the-art comparisons. The results demonstrate that (1) M-POE is robust, discriminative, and efficient; (2) GSAC-SOG is robust to outliers; (3) the proposed 3D object recognition method achieves high accuracy and robustness against clutter and occlusion, with recognition rates of 99.45%, 94.21%, and 97.88% on the U3OR, Queen, and CFV datasets, respectively.