  In this paper, we go on Rui-Xu's work on cyclotomic Birman-Wenzl algebras
$\W_{r, n}$ in \cite{RX}. In particular, we use the representation theory of
cellular algebras in \cite{GL} to classify the irreducible $\W_{r, n}$-modules
for all positive integers $r$ and $n$. By constructing cell filtrations for all
cell modules of $\W_{r, n}$, we compute the discriminants associated to all
cell modules for $\W_{r, n} $. Via such discriminats together with induction
and restriction functors given in section~5, we determine explicitly when
$\W_{r, n}$ is semisimple over a field. This generalizes our previous result on
Birman-Wenzl algebras in \cite{RS1}.
