A Smarandache-Fibonacci Triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Certainly, it is a generalization of Fibonacci sequence. A Fibonacci graceful labeling and a super Fi-bonacci graceful labeling on graphs were introduced by Kathiresan and Amutha in 2006. Generally, let G be a (p, q)-graph and S(n)|n ≥ 0 a Smarandache-Fibonacci Triple. An bi-jection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibonacci graceful graph if the induced edge labeling f∗(uv) = |f(u) −f(v)| is a bijection onto the set {S(1), S(2), . . . , S(q)}. Particularly, if S(n), n ≥ 0 is just the Fibonacci sequence Fi, i ≥ 0, such a graph is called a super Fibonacci graceful graph. In this paper, we show that some special class of graphs namely Ftn, Ctn and St m,n are super fibonacci graceful graphs.