  We investigate the existence and non-existence of maximal green sequences for
quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver
of the endomorphism algebra of a basic cluster-tilting object in the cluster
category $\mathcal{C}_\mathbb{X}$ of a weighted projective line $\mathbb{X}$.
It is proved that there exists a quiver $Q'$ in the mutation equivalence class
$\operatorname{Mut}(Q)$ such that $Q'$ admits a maximal green sequence. On the
other hand, there is a quiver in $\operatorname{Mut}(Q)$ which does not admit a
maximal green sequence if and only if $\mathbb{X}$ is of wild type.
