In this article, we give a characterization theorem for a class of corank-1 Butler groups of the form $mathcal{G}$($A_1$, ${ldots}$, $A_n$). In particular, two groups $G$ and $H$ are quasi-isomorphic if and only if there is a label-preserving bijection ${phi}$ from the edges of $T$ to the edges of $U$ such that $S$ is a circuit in T if and only if ${phi}(S)$ is a circuit in $U$, where $T$, $U$ are quasi-representing graphs for $G$, $H$ respectively.