Even　though　it　has　long　been　agreed　that　the　interest　rate　is　driven　by　a　stochastic　process,　most　of　the　existing　studies　on　dynamic　mean-downside　risk　portfolio　optimization　problem　focuses　on　deterministic　interest　rates.　This　work　investigates　a　continuous-time　mean-downside　risk　portfolio　optimization　problem　with　a　stochastic　interest　rate.　More　specifically,　we　introduce　the　Vasicek　interest　rate　model　and　choose　some　common　downside　risk　measures　to　model　our　risk　measures,　such　as,　the　lower-partial　moments(LPM),　value-at-risk(VaR)　and　conditional　value-at-risk(CVaR).　By　using　the　martingale　method　and　the　inverse　Fourier　Transformation,　we　successfully　derive　the　semi-analytical　optimal　portfolio　policies　and　the　optimal　wealth　processes　for　the　mean-downside　risk　measures　with　stochastic　interest　rate.　Finally,　we　provide　some　illustrative　examples　to　show　how　the　stochastic　interest　rate　affects　the　investment　behavior　of　investors　with　mean-downside　risk　preferences.　©　2023　Elsevier　B.V.