  In this paper we consider the $q$-Brauer algebra over $R$ a commutative
noetherian domain. We first construct a new basis for $q$-Brauer algebras, and
we then prove that it is a cell basis, and thus these algebras are cellular in
the sense of Graham and Lehrer. In particular, they are shown to be an iterated
inflation of Hecke algebras of type $A_{n-1}.$ Moreover, when $R$ is a field of
arbitrary characteristic, we determine for which parameters the $q$-Brauer
algebras are quasi-heredity. So the general theory of cellular algebras and
quasi-hereditary algebras applies to $q$-Brauer algebras. As a consequence, we
can determine all irreducible representations of $q$-Brauer algebras by linear
algebra methods.
