This paper presents a highly distinctive and robust local three-dimensional (3-D) feature descriptor named longitude and latitude spin image (LLSI). The whole procedure has two modules: local reference frame (LRF) definition and LLSI feature description. We employ the same technique as Tombari to define the LRF. The LLSI feature descriptor is obtained by stitching the longitude and latitude (LL) image to the original spin image vertically, where the LL image was generated similarly with the spin image by mapping a two-tuple into a discrete two-dimensional histogram. The performance of the proposed LLSI descriptor was rigorously tested on a number of popular and publicly available datasets. The results showed that our method is more robust with respect to noise and varying mesh resolution than existing techniques. Finally, we tested our LLSI-based algorithm for 3-D object recognition on two popular datasets. Our LLSI-based algorithm achieved recognition rates of 100%, 98.2%, and 96.2%, respectively, when tested on the Bologna, University of Western Australia (UWA) (up to 84% occlusion), UWA datasets (all). Moreover, our LLSI-based algorithm achieved 100% recognition rate on the whole UWA dataset when generating the LLSI descriptor with the LRF proposed by Guo.