This paper proposes a novel protein structure descriptor (or representation) and its application for structure comparison. Since the functions of protein may come from its structure, the method of measuring structural similarities between two proteins can infer their functional closeness. In this paper, we have developed a novel descriptor (3D edge histogram) to compare the structures of proteins. The 3D edge histogram is a local distribution of bonds between the atoms in a protein. We have designed and implemented a protein structure retrieval system based on the 3D edge histogram to demonstrate that it could be effective in protein structure comparison. In this system, principal component analysis for aligning, voxelization for volume generation, quantization, 3D edge extraction, and comparison of 3D edge histogram are performed. The protein structure retrieval system using the 3D edge histogram shows fast retrieval with relatively precise results. It can be used for pre-screening purposes with a huge database.