  A chiral field theory of $0^{-+}$ glueball is presented. By adding a $0^{-+}$
glueball field to a successful Lagrangian of chiral field theory of
pseudoscalar, vector, and axial-vector mesons, the Lagrangian of this theory is
constructed. The couplings between the pseodoscalar glueball field and mesons
are via U(1) anomaly revealed. Qualitative study of the physical processes of
the $0^{-+}$ glueball of $m=1.405\textrm{GeV}$ is presented. The theoretical
predictions can be used to identify the $0^{-+}$ glueball.
