We investigate the entropy squeezing of a two-level atom in the Jaynes-Cummings model,and provide a scheme to generate the sustained optimal entropy squeezing of the atom via non-Hermitian operation.Our results show that the squeezing degree and the persistence time of entropy squeezing of atomic polarization components greatly depend on the non-Hermiticity intensity in non-Hermitian operation.Especially,under a proper choice of non-Hermiticity parameters,the sustained optimal entropy squeezing of the atom can be generated even though the atom is initially prepared in a no entropy squeezing state.