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The author is mainly interest in the Gr\"{o}bner-Shirshov bases of finiteCoxeter groups. It is known that the finite Coxeter groups are classified interms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mentionthat the presentation of group determines the Gr\"{o}bner-Shirshov bases ofgroup. In this paper, the author rearranges the generators, marks them onCoxeter-Dynkin diagrams, and gets a simple presentation of theGr\"{o}bner-Shirshov bases for Coxeter groups of types $G_2, F_4, E_6$ and$E_7$. This article also gives the Gr\"{o}bner-Shirshov basis of Coxeter groupof type $E_8$.

Gr\"obner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$