Beta-Exponential　Distribution　(BED)　is　proposed　by　Nadarajah　and　Samuel　Kotz　which　contains　several　well-known　distributions.　With　the　addition　of　two　shape　parameters,　this　distribution　can　fit　a　wider　range　of　data　and　therefore　has　been　widely　used　in　life　testing.　However,　there　are　few　literature　on　the　properties　of　order　statitics　from　this　distribution,　especially　the　best　linear　unbiased　estimation　(BLUE)　of　the　location-scale　parameters.　In　this　paper,　a　new　algorithm　is　proposed　by　us　to　obtain　closed-form　expression　for　variance-covariance　matrix　of　order　statistics　from　this　distribution　and　give　the　BLUE　for　the　location-scale　parameters　for　the　first　time.　Compared　with　several　other　classical　parameter　estimation　methods　(MLE,　trimmed　L-moments　(TL-moments),　probability　weighted　moments　(PWM)),　BLUE　is　more　suitable　for　location-scale　parameter　estimation　under　small　sample　size　for　this　distribution.　Besides,　the　explicit　expressions　for　moments　of　order　statistics　under　the　independent　identically　distributed　(IID)　case　and　independent　not　identically　distributed　(INID)　case　are　also　derived.　Furthermore,　for　BED　with　three　parameters　(two　shape　parameters　and　scale　parameter),　we　propose　an　improved　TL-moments　estimation　method　based　on　order　statistics　isotone　transformation　under　two　different　trimmed　schemes　(s=　t=　1　and　s=　1　,　t=　0)　as　well　as　an　improved　PWM　estimation　method　and　conduct　simulation　study　to　compare　the　performance　of　each　new　method　with　MLE.　As　a　result,　the　improved　TL-moments　estimation　(s=　t=　1)　and　the　improved　PWM　estimation　perform　better　than　MLE　on　the　whole.　©　2023,　School　of　Mathematical　Sciences,　University　of　Science　and　Technology　of　China　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.