  We present the construction of the classical Batalin-Vilkovisky action for
topological Dirac sigma models. The latter are two-dimensional topological
field theories that simultaneously generalise the completely gauged
Wess-Zumino-Novikov-Witten model and the Poisson sigma model. Their underlying
structure is that of Dirac manifolds associated to maximal isotropic and
integrable subbundles of an exact Courant algebroid twisted by a 3-form. In
contrast to the Poisson sigma model, the AKSZ construction is not applicable
for the general Dirac sigma model. We therefore follow a direct approach for
determining a suitable BV extension of the classical action functional with
ghosts and antifields satisfying the classical master equation. Special
attention is paid on target space covariance, which requires the introduction
of two connections with torsion on the Dirac structure.
