Feature description for the 3D local shape in the presence of noise, varying mesh resolutions, clutter and occlusion is a quite challenging task in 3D computer vision. This paper tackles the problem by proposing a new local reference frame (LRF) together with a novel triple orthogonal local depth images (TOLDI) representation, forming the TOLDI method for local shape description. Compared with previous methods, TOLDI manages to perform efficient, distinctive and robust description for the 3D local surface simultaneously under various feature matching contexts. The proposed LRF differs from many prior ones in its calculation of the z-axis and x-axis, the z-axis is calculated using the normal of the keypoint and the x-axis is computed by aggregating the weighted projection vectors of the radius neighbors. TOLDI feature descriptors are then obtained by concatenating three local depth images (LDI) captured from three orthogonal view planes in the LRF into feature vectors. The performance of our TOLDI approach is rigorously evaluated on several public datasets, which contain three major surface matching scenarios, namely shape retrieval, object recognition and 3D registration. Experimental results and comparisons with the state-of-the-arts validate the effectiveness, robustness, high efficiency, and overall superiority of our method. Our method is also applied to aligning 3D object and indoor scene point clouds obtained by different devices (i.e., LiDAR and Kinect), the accurate outcomes further confirm the effectiveness of our method.