Let G be a graph with p vertices and q edges.A decomposition of G is a collection , such that are edge disjoint and every edge in belongs to G.If each is a Tribonacci graceful graph, then is called a Tribonacci graceful decomposition of G.The minimum cardinality of a Triboonacci graceful decomposition of G is called the Tribonacci graceful decomposition number of G and is denoted by .In this paper, we investigate the bounds of Tribonacci graceful decomposition of Diamond Snake graph , Mongolian tent graph and Triangular Diamond graph