  We construct the Dirac-Born-Infeld (DBI) action of a real linear multiplet in
4D $\mathcal{N}=1$ supergravity. Based on conformal supergravity, we derive the
general condition under which the DBI action can be realized, and show that it
can be constructed in the new minimal supergravity. We also generalize it to
the matter coupled system.
