This　paper　mainly　proposes　a　new　model　for　stock　markets,　namely　a　portfolio　selection　model　with　interval-valued　return　rates.　To　do　it,　we　review　some　concepts　of　interval　numbers　and　the　acceptability　function　of　rankings　at　first.　And　we　present　an　improved　ranking　method　for　intervals.　Then,　we　introduce　set-valued　random　variables,　the　semi-variance　and　the　semi-covariance　of　interval-valued　random　variables　and　prove　some　related　properties.　After　the　preparation,　we　introduce　our　new　portfolio　selection　model　of　interval-valued　return　rates　with　semi-variances　as　risk　measurements　of　stocks.　Finally,　we　do　an　empirical　analysis　by　using　real　stock　data　in　NASDAQ　stock　market　to　illustrate　our　model.