Computers store data in the form of bit or binary digits. Gray code is a reflected binary code, which is an ordering of the binary numeral system such that two successive values differ by only one bit (binary digit). The hamming distance is a metric used to compare two binary strings of equal length and is defined as the number of bit positions in which the two binary strings differ. The hamming distance between two binary strings 𝑎 and b of equal length is denoted by hd(𝑎, b). It is used for error detection in data transmission and in coding theory. In this paper, we define a new labeling called gray code hamming distance labeling. The existence of gray code hamming distance labeling of M- join of Comb graph, H- graph, and Twig graph were discussed and their gray code hamming distance number were obtained.