  Let $K$ be a field and $q\in K$, $q\neq 0, 1$. Let $\mathcal {H}_n(q, Q)$ be
an Ariki-Koike algebra, where the cyclotomic parameter $Q=(Q_1, Q_2, \cdots,
Q_r)\in K^r$ with $r\geq 2$, $Q_i=q^{a_i}$, $a_i\in \mathbb{Z}$. For a weight
one block $B$ of $\mathcal {H}_n(q, Q)$, we prove in this paper that
$\text{rad}\:B=I$, where $I$ is the nilpotent ideal constructed for a symmetric
cellular algebra in [Radicals of symmetric cellular algebras, Colloq. Math.
{\bf 133} (2013) 67-83]. We also give some applications of this result.
