For a graph \(G\), the line graph \(L(G)\) is a graph such that the vertex set of \(L(G)\) is identical with the edge set of \(G\), and two distinct vertices \(e_2\) and \(e_2\) of \(L(G)\) are adjacent in \(L(G)\) if and only if \(|e_1\cap e_2|=1\) in \(G\). The author of this paper tries to classify all finite commutative rings \(R\) whose zero-divisor graph \(\Gamma(R)\) is either a line graph or such that \(\overline{\Gamma(R)} \) is a line graph. This is achieved in Theorem \(2.11\) for classifying all finite commutative rings \(R\) whose \(\Gamma(R)\) is a line graph. In order to classify all finite commutative rings \(R\) whose \(\overline{\Gamma(R)}\) is a line graph, the set of finite commutative rings are divided into two disjoint subsets, i.e., the local rings and the nonlocal rings. The nonlocal case is treated in Theorem \(3.2\), and a complete algebraic classification is got, which is relatively easy after applying the structure theorem of Artinian rings. While the difficult local case is settled in Theorem \(3.8\), which is classified half graph-theoretically and the other half is algebraic.