The　moving　least-squares　(MLS)　method　has　been　developed　for　fitting　measurement　data　contaminated　with　errors.　The　local　approximants　of　the　MLS　method　only　take　the　random　errors　of　the　dependent　variable　into　account,　whereas　the　independent　variables　of　measurement　data　always　contain　errors.　To　consider　the　influence　of　errors　of　dependent　and　independent　variables,　the　moving　total　least-squares　(MTLS)　method　is　a　better　choice.　However,　both　MLS　and　MTLS　methods　are　sensitive　to　outliers,　greatly　affecting　fitting　accuracy　and　robustness.　This　paper　presents　an　improved　method,　the　trimmed　MTLS　(TrMTLS)　method,　in　which　the　total　least-squares　method　with　a　truncation　procedure　is　adopted　to　determine　the　local　coefficients　in　the　influence　domain.　This　method　can　deal　with　outliers　and　random　errors　of　all　variables　without　setting　the　threshold　or　adding　small　weights　subjectively.　The　results　of　numerical　simulation　and　experimental　measurements　indicate　that　the　proposed　algorithm　has　better　fitting　accuracy　and　robustness　than　the　MTLS　and　MLS　methods.　©　2020　IOP　Publishing　Ltd.