  Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface
$S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with
$C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.
