  We consider the symplectic group $\mathrm{Sp}_{2n}$ defined over a $p$-adic
field $F$, where $p=2$. We prove that every simple supercuspidal representation
(in the sense of Gross--Reeder) of $\mathrm{Sp}_{2n}(F)$ corresponds to an
irreducible $L$-parameter under the local Langlands correspondence for
$\mathrm{Sp}_{2n}$ established by Arthur.
