  In this article, we investigate the representations of the Drinfeld doubles
$D(R_{mn}(q))$ of the Radford Hopf algebras $R_{mn}(q)$ over an algebraically
closed field $\Bbbk$, where $m>1$ and $n>1$ are integers and $q\in\Bbbk$ is a
root of unity of order $n$. Under the assumption ${\rm char}(\Bbbk)\nmid mn$,
all the finite dimensional indecomposable modules over $D(R_{mn}(q))$ are
displayed and classified up to isomorphism. The Auslander-Reiten sequences in
the category of finite dimensional $D(R_{mn}(q))$-modules are also all
displayed. It is shown that $D(R_{mn}(q))$ is of tame representation type.
