In　this　paper,　we　propose　a　protocol　to　generate　steady　Greenberger–Horne–Zeilinger　(GHZ)　states　of　three　Rydberg　atoms　with　dissipation　dynamics　and　simplified　Lyapunov　control.　Firstly,　combining　with　the　dissipation　dynamics　and　Rydberg　antiblockade,　a　unique　and　steady　solution　of　the　master　equation　of　the　system　is　obtained.　Furthermore,　to　polish　the　convergence　rate,　we　add　well-designed　additional　coherent　control　(ACC)　fields　with　Lyapunov　control　into　the　traditional　dissipation　process　and　simplify　the　control　fields　with　bang–bang　design　proposed　in　the　Ref.　(Hou　et　al.,　2012)　for　better　experimental　feasibility.　Numerical　simulation　reveals　that　the　GHZ　states　generation　is　prominently　accelerated　and　the　simplified　control　fields　have　the　similar　efficiency　with　the　traditional　Lyapunov　control　fields　but　are　easier　to　realize　in　realistic　situations.　We　hope　this　work　could　provide　an　alternative　way　to　polish　the　generation　of　entanglement.　©　2020　Elsevier　B.V.