  In this paper, we present a new class of charged rotating black brane
solutions in the higher dimensional Brans-Dicke-Born-Infeld theory and
investigate their properties. Solving the field equations directly is a
non-trivial task because they include the second derivatives of the scalar
field. We remove this difficulty through a conformal transformation. Also, we
find that the suitable Lagrangian of Einstein-Born-Infeld-dilaton gravity is
not the same as presented in \cite{DHSR}. We show that the given solutions can
present black brane, with inner and outer event horizons, an extreme black
brane or a naked singularity provided the parameters of the solutions are
chosen suitably. These black brane solutions are neither asymptotically flat
nor (anti)-de Sitter. Then we calculate finite Euclidean action, the conserved
and thermodynamic quantities through the use of counterterm method. Finally, we
argue that these quantities satisfy the first law of thermodynamics, and the
entropy does not follow the area law.
