In 2004, Blinco et al. [1] introduced the notion of γ-labeling. A function h defined on the vertex set of a graph G with n edges is called a γ-labeling if (i) h is a ρ-labeling of G (ii) G is tripartite with vertex tripartition (A, B, C) with C = {c} and b ∈ B such that (b, c) is the unique edge joining an element of B to c (iii) for every edge (a, v) ∈ E(G) with a ∈ A, h(a) < h(v) (iv) h(c) − h(b) = n. In [1], they have also proved a significant result on graph decomposition that if a graph G with n edges admits a γ-labeling, then the complete graph K2cn+1 can be cyclically decomposed into 2cn + 1 copies of the graph G, where c is any positive integer. Motivated by the result of Blinco, in this paper, we prove that the almost-bipartite graph obtained from the grid Pm× Pnby adding a path of length three, P4 between the first pair of diagonally nonadjacent vertices of the grid Pm× Pn, denoted (Pm× Pn) ⊕ P4 admits a γ-labeling. © 2014 Pushpa Publishing House, Allahabad, India