A function $f$ is called a $F$-Geometric mean labeling of a graph $G(V,E)$ if $f:V(G)\rightarrow\{1,2,3,\dots,q+1\}$ is injective and the induced function $f^*:E(G)\rightarrow\{1,2,3,\dots,q\}$ defined as $f^*(uv)=\left\lfloor \sqrt{f(u)f(v)} \right\rfloor,$ for all $uv\in E(G),$ is bijective. A graph that admits a $F$-Geometric mean labelling is called a $F$-Geometric mean graph. In this paper, we have discussed the $F$-Geometric mean labeling of some chain graphs and thorn graphs.