Let G = (V, E) be a graph. The onto minus edge dominating function is a function f: E → {−1, 0, 1} such that f is onto and f (N [e]) ≥ 1 for all e ∈ E(G). The onto minus edge domination number of a graph G is a minimum weight of a set of onto minus edge dominating functions on G and it is denoted by γ^' om (G). In this paper we discuss about the onto minus edge domination number of Paths, Cycles and Bipartite graph.