The idea of an overlapping rectangular region coding of binary images inspired the overlapping rectangular non-symmetry, the anti-packing pattern representation model (RNAM), and the extended Gouraud shading approach. A novel lossy gray image representation algorithm based on the overlapping RNAM, which is called ORNAMC representation algorithm, is proposed. Also, the four principles for anti-packing the overlapping homogenous blocks are presented in this paper. In the proposed ORNAMC representation algorithm, the wrong decoding problem of the matrix R for the overlapping RNAM representation of gray images is solved separately by using the horizontal, vertical, and isolated matrices, i.e.,H, V and I. These are used to identify the vertex types instead of using a single hybrid matrix, i.e., R. In addition, by redefining the codeword set for the three vertices symbols, this paper proposed a new coordinate data compression algorithm for coding the coordinates of all non-zone elements in the three matrices H, V and I. By taking some idiomatic standard gray images in the field of image processing as typical test objects, and by comparing the proposed ORNAMC representation algorithm with the latest non-overlapping RNAMC, the experimental results show that the former has a higher compression ratio and a fewer number of blocks and yet, maintains image quality. Therefore, a better method is to represent the gray image.