  Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory
where the tangent group is taken to be the pseudo-unitary group instead of the
orthogonal group. A Higgs mechanism for massive gravity was also formulated. We
generalize this construction to obtain massive Hermitian gravity with the use
of a complex Higgs multiplet. We show that both the graviton and antisymmetric
tensor acquire the same mass. At the linearized level, the theory is ghost free
around Minkowski background and describes a massive graviton with five degrees
of freedom and an antisymmetric field with three degrees of of freedom. We
determine the strong coupling scales for these degrees of freedom and argue
that the potential nonlinear ghosts, if they exist, have to decouple from the
gravitational degrees of freedom in strong coupling regime.
