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It's well known that every planar graph is $4$-colorable. A toroidal graph isa graph that can be embedded on a torus. It's proved that every toroidal graphis $7$-colorable. A proper coloring of a graph is called \emph{odd} if everynon-isolated vertex has at least one color that appears an odd number of timesin its neighborhood. The smallest number of colors that admits an odd coloringof a graph $ G $ is denoted by $\chi_{o}(G)$. In this paper, we prove that if$G$ is tortoidal, then $\chi_{o}\left({G}\right)\le9$; Note that $K_7$ is atoroidal graph, the upper bound is no less than $7$.

The odd chromatic number of a toroidal graph is at most 9