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