This　article　is　concerned　with　the　reconstruction　of　contaminated　measurement　data　based　on　the　moving　total　least　squares　(MTLS)　method,　which　is　extensively　applied　to　many　engineering　and　scientific　fields.　Traditional　MTLS　method　is　lack　of　robustness　and　sensitive　to　the　outliers　in　measurement　data.　Based　on　the　framework　of　MTLS　method,　we　proposed　a　robust　MTLS　method　called　RMTLS　method　by　introducing　a　two-step　pre-process　to　detect　and　remove　the　anomalous　nodes　in　the　support　domain.　The　first　step　is　an　iterative　regression　procedure　that　combines　with　k-medoids　clustering　to　automatically　reduce　the　weight　of　anomalous　node　for　a　regression-based　reference　(curve　or　surface).　Based　on　the　distances　between　reference　and　discrete　points,　the　second　step　adopts　a　density　function　defined　by　a　sorted　distance　sequence　to　select　the　normal　points　without　setting　a　threshold　artificially.　After　the　two-step　pre-process,　weighted　total　least　square　is　performed　on　the　selected　point　set　to　obtain　the　estimation　value.　By　disposing　of　the　anomalous　nodes　in　each　independent　support　domain,　multiple　outliers　can　be　suppressed　within　the　whole　domain.　Furthermore,　the　suppression　of　multiple　continual　outliers　is　possible　by　adopting　asymmetric　support　domain　and　introducing　previous　estimation　points.　The　proposed　method　shows　great　robustness　and　accuracy　in　reconstructing　the　simulation　and　experiment　data.　©　2021　Elsevier　Ltd