Let G be a finite, simple, undirected and non-trivial graph. A fuzzy graph is said to admit tri-magic labeling if the number of magic membership values $K_i$'s and $K_j$'s ($1 \le i \le 3$) differs by at most 1 and $|K_i - K_j| \le \frac{2}{10^r}$ for $1\le i, j \le 3$, $r \ge 2$. The fuzzy graph which admits a tri-magic labeling is called a fuzzy tri-magic labeling graph. The fuzzy tri-magic labeling graphs are denoted by $\tilde{T}_{m0}G$. In this paper it is proved that the generalized Jahangir graph $JG_{n,m}$ is Fuzzy tri-magic $n \ge 2$ and $m \ge 3$.