  Weyl invariant gravity has been investigated as the fundamental theory of the
vector inflation. Accordingly, we consider a Weyl invariant extension of
Dirac-Born-Infeld type gravity. We find that an appropriate choice of the
metric removes the scalar degree of freedom which is at the first sight
required by the local scale invariance of the action, and then a vector field
acquires mass. Then nonminimal couplings of the vector field and curvatures are
induced. We find that the Dirac-Born-Infeld type gravity is a suitable theory
to the vector inflation scenario.
