Solid　tumors　are　heterogeneous　in　composition.　Cancer　stem　cells　(CSCs)　are　a　highly　tumorigenic　cell　type　found　in　developmentally　diverse　tumors　that　are　believed　to　be　resistant　to　standard　chemotherapeutic　drugs　and　responsible　for　tumor　recurrence.　Thus　understanding　the　tumor　growth　kinetics　is　critical　for　development　of　novel　strategies　for　cancer　treatment.　In　this　paper,　the　moment　stability　of　nonlinear　stochastic　systems　of　breast　cancer　stem　cells　with　time-delays　has　been　investigated.　First,　based　on　the　technique　of　the　variation-of-constants　formula,　we　obtain　the　second　order　moment　equations　for　the　nonlinear　stochastic　systems　of　breast　cancer　stem　cells　with　time-delays.　By　the　comparison　principle　along　with　the　established　moment　equations,　we　can　get　the　comparative　systems　of　the　nonlinear　sto-chastic　systems　of　breast　cancer　stem　cells　with　time-delays.　Then　moment　stability　theorems　have　been　established　for　the　systems　with　the　stability　properties　for　the　comparative　systems.　Based　on　the　linear　matrix　inequality　(LMI)　technique,　we　next　obtain　a　criteria　for　the　exponential　stability　in　mean　square　of　the　nonlinear　stochastic　systems　for　the　dynamics　of　breast　cancer　stem　cells　with　time-delays.　Finally,　some　numerical　examples　are　presented　to　illustrate　the　efficiency　of　the　results.