  We construct a Dirac-Born-Infeld (DBI) action coupled to a two-form field in
four dimensional $\mathcal{N}=1$ supergravity. Our superconformal formulation
of the action shows a universal way to construct it in various Poincar\'e
supergravity formulations. We generalize the DBI action to that coupled to
matter sector. We also discuss duality transformations of the DBI action, which
are useful for phenomenological and cosmological applications.
