Assume that U is a left R-semimodule, R is an abelian semiring with nonzero identity. The co-intersection graphs of U, indicated by G(U), an undirected graph whose nods set is the collection of all non-trivial subsemimodules of U with two distinct nods X, Y are adjacent if and only if X + Y ≠ U. These graphs was studies to relate the combinatorial possessions of G(U) to the algebraic possessions of the R-semimodule U. Connectedness and planarity were for G(U). Also, studies are done on the girth, diameter, clique and chromatic number of this graphs.