The　famous　mean-variance　portfolio　selection　model　introduced　by　Markowitz　in　[7]　is　an　important　breakthrough　in　mathematical　finance,　which　deals　with　uncertainties　appearing　in　financial　markets.　In　real　financial　market,　there　may　exist　two　kinds　of　uncertainties.　One　is　randomness　and　the　other　is　impreciseness　or　vagueness.　In　this　paper　we　study　the　portfolio　selection　problem　combining　randomness　with　impreciseness　by　considering　asset　return　rates　and　risks　as　random　intervals　and　propose　two　models.　For　these　models　it　is　important　to　give　a　suitable　ordering　for　intervals.　Here　we　use　gamma-index　and　satisfactory　crisp　equivalent　system　to　do　it　given　by　Sengupta　et　al.　in　[11].　As　an　application　of　our　models,　a　numerical　example　is　given　whose　data　comes　from　a　real　stock　market.