Abstract: Hamming gracefulness of graphs problem, in computer networks graceful embedding aspect, has the good application value and the broad research prospect. So far, few related works has been done in domestic and abroad. Therefore, we introduce and establish the labeling function method to prove that the graphs G+C₄ were hamming-graceful, which hamming-graceful graph G random vertex hangs a circuit C₄ obtained graphs. An important conclusion was proved from this all connections quadrilateral cactus graph are hamming-graceful graphs in which graph C₄ is an 4-vertex circuit.