Let \(K_{m} – H\) denote the graph obtained from the complete graph on \(m\) vertices, \(K_{m}\), by removing the edge set \(E(H)\) of \(H\), where \(H\) is a subgraph of \(K_{m}\). In this paper, we characterize the potentially \(K_{6} – 3K_{2}\)-graphic sequences, where \(pK_{2}\) is a matching consisting of \(p\) edges.