A graph G=(V,E,ϕ) with p vertices and q edges is called Fibonacci graceful graph [FGG] if a function ϕ isdefined as ϕ:V(G)→{0,1,2,…,F_q }and the induced edge labeling ϕ^*:E→{F_1,F_(2,) F_3,…,F_q } defined as ϕ^* (uv)=|ϕ(u)-ϕ(v)| is bijective. In this article an examine is done with Fibonacci graceful labeling [FGL] for some special graphs. AMS Classification : 05C78