  Let $G$ be a finite group and $p$ be a prime number dividing the order of
$G$. An irreducible character $\chi$ of $G$ is called a quasi $p$-Steinberg
character if $\chi(g)$ is nonzero for every $p$-regular element $g$ in $G$. In
this paper, we classify quasi $p$-Steinberg characters of the complex
reflection groups $G(r,q,n)$. In particular, we obtain this classification for
Weyl groups of type $B_n$ and type $D_n$.
