The $2$-closure $\overline{G}$ of a permutation group $G$ on $Ω$ is defined to be the largest permutation group on $Ω$, having the same orbits on $Ω\timesΩ$ as $G$. It is proved that if $G$ is supersolvable, then $\overline{G}$ can be found in polynomial time in $|Ω|$. As a byproduct of our technique, it is shown that the composition factors of $\overline{G}$ are cyclic or alternating of prime degree.