This paper presents a novel local surface descriptor by encoding the neighboring points' position angles of a key point into a histogram. The generation of the feature descriptor is simple and efficient. Firstly, we construct a Local Reference Frame (LRF) by performing eigenvalue decomposition on a scatter covariance matrix. Then, the sphere support of the key point is divided into several sphere shells. In each sphere shell, we calculate the angles between a neighboring point and z-axis, x-axis respectively. Subsequently, the cosine values of these two angles are mapped into two 1D histograms respectively. Finally, all the 1D histograms are put together followed by a normalization to form the descriptor. Our proposed local surface descriptor is called Signature of Position Angles Histograms (SPAH). As for a point cloud with color information, the SPAH can easily be extended to a Color SPAH (CSPAH) descriptor only by adding one more 1D histogram generated by the color information in each sphere shell. The performance of the proposed SPAH was tested on the Bologna Dataset 1 to compare with several state-of-the-art feature descriptors. The experiment results show that our SPAH descriptor is more robust to noise and vary mesh decimations. Moreover, our SPAH and CSPAH descriptors based 3D object recognition algorithms achieved a good performance on the Bologna Dataset 3.