  In a Banach algebra, we introduce a new type of generalized inverse called
g$\pi$-Hirano inverse. Firstly, several existence criteria and the equivalent
definition of this inverse are investigated. Then, we discuss the relationship
between the g$\pi$-Hirano invertibility of $a$, $b$ and that of the sum $a+b$
under some weaker conditions. Finally, as applications to the previous additive
results, some equivalent characterizations for the g$\pi$-Hirano invertibility
of the anti-triangular matrix over Banach algebras are obtained.In particular,
some results in this paper are different from the corresponding ones of
classical generalized inverses, such as Drazin inverse and generalized Drazin
inverse.
