We　generalize　the　quantum　adiabatic　theorem　to　the　non-Hermitian　system　and　build　a　strict　adiabaticity　condition　to　make　the　adiabatic　evolution　nonlossy　when　taking　into　account　the　effect　of　the　adiabatic　phase.　According　to　the　strict　adiabaticity　condition,　the　nonadiabatic　couplings　and　the　effect　of　the　imaginary　part　of　adiabatic　phase　should　be　eliminated　as　much　as　possible.　Also,　the　non-Hermitian　Hamiltonian　reverse-engineering　method　is　proposed　for　adiabatically　driving　an　artificial　quantum　state.　A　concrete　two-level　system　is　adopted　to　show　the　usefulness　of　the　reverse-engineering　method.　We　obtain　the　desired　target　state　by　adjusting　extra　rotating　magnetic　fields　at　a　predefined　time.　Furthermore,　the　numerical　simulation　shows　that　certain　noise　and　dissipation　in　the　systems　are　no　longer　undesirable　but　play　a　positive　role　in　the　scheme.　Therefore,　the　scheme　is　quite　useful　for　quantum　information　processing　in　some　dissipative　systems.　©　2016　American　Physical　Society.