In this paper we will show that there does not exist a distance-regular graph $Γ$ with intersection array $\{80, 54,12; 1, 6, 60\}$. We first show that a local graph $Δ$ of $Γ$ does not contain a coclique with 5 vertices, and then we prove that the graph $Γ$ is geometric by showing that $Δ$ consists of 4 disjoint cliques with 20 vertices. Then we apply a result of Koolen and Bang to the graph $Γ$, and we could obtain that there is no such a distance-regular graph.