In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $widehat{{Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $widehat{{Gamma}_I(N)}$ are connected by a path of length at most 3, and if $widehat{{Gamma}_I(N)}$ contains a cycle, then the core K of $widehat{{Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $widehat{{Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.