Summary: The pebbling number of a graph \(G, f(G)\), is the least \(n\) such that, no matter how \(n\) pebbles are placed on the vertices of \(G\), we can move a pebble to any vertex by a sequence of pebbling moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Let \(p_{1},p_{2},\dots,p_n\) be positive integers and \(G\) be such a graph, \(V(G)=n\). The thorn graph of the graph \(G\), with parameters \(p_{1},p_{2},\dots,p_n\), is obtained by attaching \(p_i\) new vertices of degree 1 to the vertex \(u_i\) of the graph \(G\), \(i=1,2,\dots,n\). Graham conjectured that for any connected graphs \(G\) and \(H\), \(f(G\times H) \leq f(G)f(H)\). We show that Graham’s conjecture holds true for a thorn graph of the complete graph with every \(p_i>1\) (\(i=1,2,\dots,n\)) by a graph with the two-pebbling property. As a corollary, Graham’s conjecture holds when \(G\) and \(H\) are the thorn graphs of the complete graphs with every \(p_i>1\) (\(i=1,2,\dots,n\)).