Summary: Let \(S\) be a non-empty set of positive integers. We define the set-prime graph \(G_S(\Gamma)\) of a given finite group \(\Gamma\) of order \(n\) with respect to \(S\), as a graph with vertex set \(V(G_S(\Gamma))= \Gamma\) and any two vertices \(a\) and \(b\) are adjacent in \(G_S (\Gamma)\) if and only if \((o(a),o(b))\in S\). In this paper, we observe that order prime and general order prime graphs are special cases of set-prime graphs and we investigate some properties of set-prime graphs of finite groups.