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In this paper we will show that there does not exist a distance-regular graph$\Gamma$ with intersection array $\{80, 54,12; 1, 6, 60\}$. We first show thata local graph $\Delta$ of $\Gamma$ does not contain a coclique with 5 vertices,and then we prove that the graph $\Gamma$ is geometric by showing that $\Delta$consists of 4 disjoint cliques with 20 vertices. Then we apply a result ofKoolen and Bang to the graph $\Gamma$, and we could obtain that there is nosuch a distance-regular graph.

There does not exist a distance-regular graph with intersection array $\{80, 54,12; 1, 6, 60\}$