We　propose　a　fast　and　dephasing-tolerant　scheme　for　the　preparation　of　steady　Knill-Laflamme-Milburn　(KLM)　state　between　a　pair　of　Rydberg　atoms　by　dissipation.　In　this　scheme,　arbitrary　initial　state　can　be　engineered　to　the　KLM　state　with　high　fidelity　(99.24%).　Compared　to　most　schemes　based　on　Rydberg　dissipation　dynamics,　the　time　to　prepare　steady　state　can　be　significantly　reduced　in　our　scheme　(80　mu,$)　due　to　the　use　of　strong　resonant　dipole-dipole　interactions.　In　addition,　the　scheme　can　effectively　suppress　the　dephasing　error　of　the　Rydberg　atoms　caused　by　interatomic　distance　fluctuations,　which　may　severely　disrupt　the　desired　systematic　dynamics.　Thus　the　present　scheme　is　of　interest　and　deserves　further　experimental　investigation　to　enrich　the　dissipation　dynamics　based　on　the　Rydberg　atoms.