In　many　fields,　limited　or　censored　data　are　often　collected　due　to　limitations　of　measurement　equipment　or　experimental　design.　Commonly　used　censored　linear　regression　models　rely　on　the　assumption　of　normality　for　the　error　terms.　However,　this　approach　has　faced　criticism　in　literature　due　to　its　sensitivity　to　deviations　from　the　normality　assumption.　In　this　paper,　we　propose　an　extension　of　the　CR　model　under　the　two-piece　generalized　t　(TPGT)-error　distribution,　called　TPGT-CR　model.　The　TPGT-CR　model　offers　greater　flexibility　in　modeling　data　by　accommodating　skewness　and　heavy　tails.　We　developed　a　modified　maximum　likelihood　(MML)　estimator　for　the　proposed　model　and　introduced　the　modified　deviance　residual　to　detect　outliers.　The　developed　MML　estimator　under　the　TPGT　assumption　possesses　several　appealing　merits,　including　robustness　against　outliers,　asymptotic　equivalence　to　the　maximum　likelihood　estimator,　and　explicit　functions　of　sample　observations.　Simulation　studies　are　conducted　to　examine　the　finite　sample　performance,　robustness,　and　effectiveness　of　both　the　classical　and　proposed　estimators.　The　results　from　both　the　simulated　and　real　data　illustrate　the　usefulness　of　the　proposed　method.