  We consider the ADM formalism of the Brans-Dicke theory and propose an
anisotropic extension of the theory by introducing five free parameters. We
find that the resulting theory reveals many interesting aspects which are not
present in the original BD theory. We first discuss the ghost instability and
strong coupling problems which are present in the gravity theory without the
full diffeomorphism symmetry and show that they can be avoided in a region of
the parameter space. We also perform the post-Newtonian approximation and show
that the constraint of the Brans-Dicke parameter $\omega_{{\rm BD}}$ being
large to be consistent with the solar system observations could be evaded in
the extended theory. We also discuss that accelerating Universe can be achieved
without the need of the potential for the Brans-Dicke scalar.
