Thetime-delaysignature(TDS)ofchaosoutputina1550nmvertical-cavitysurface-emittinglaser(VCSEL)subjecttofiberBragggrating(FBG)feedbackisinvestigatedexperimentally.Autocorrelationfunction(ACF)andmutualinformation(MI)areusedforquantitativelyidentifyingtheTDSofchaos.Forvariousbiascurrents,theTDSevolutionwiththefeedbackstrengthisdifferent,astheFBGprovideswavelength-selectivefeedback.Furthermore,basedontheTDSmapoftheFBGfeedbackVCSEL(FBGF-VCSEL)intheparameterspaceoffeedbackstrengthandbiascurrent,theoptimalTDSsuppressionregions,wherethedominantpolarizationmodeofFBGF-VCSELlocatesattheedgeofthemainlobeofFBGreflectionspectrum,havebeendetermined.Finally,forcomparativepurpose,theTDSofchaosinmirrorfeedbackVCSEL(MF-VCSEL)alsohasbeenpresented,andtheresultsshowthatanFBGF-VCSELpossessesbetterTDSsuppressionperformancethananMF-VCSEL.