It　is　still　a　challenge　to　experimentally　realize　shortcuts　to　adiabaticity　(STA)　for　a　non-Hermitian　quantum　system　since　a　non-Hermitian　quantum　system＇s　counterdiabatic　driving　Hamiltonian　contains　some　unrealizable　auxiliary　control　fields.　In　this　paper,　we　relax　the　strict　condition　in　constructing　STA　and　propose　a　method　to　redesign　a　realizable　supplementary　Hamiltonian　to　construct　non-Hermitian　STA.　The　redesigned　supplementary　Hamiltonian　can　be　eithersymmetric　or　asymmetric.　For　the　sake　of　clearness,　we　apply　this　method　to　an　Allen-Eberly　model　as　an　example　to　verify　the　validity　of　the　optimized　non-Hermitian　STA.　The　numerical　simulation　demonstrates　that　a　ultrafast　population　inversion　could　be　realized　in　a　two-level　non-Hermitian　system.　©　2017　by　WILEY-VCH　Verlag　GmbH　&　Co.　KGaA,　Weinheim