Uncertainty　is　present　in　real　financial　markets　due　to　unknown　events,　such　as　return　streams,　prices　of　securities,　maintenance　costs　etc.　Usually,　uncertainty　includes　two　aspects:　randomness　and　fuzziness.　Famous　Markowitz＇s　portfolio　selection　model　deals　with　uncertainty　using　probability　approach.　But　it　is　not　enough　to　describe　the　real　financial　markets.　This　paper　considers　the　return　rate　as　a　fuzzy　number　and　assume　all　investors　are　risk　averse,　who　make　investment　decisions　according　to　maximize　utility　score.　The　score　is　given　by　the　Von-Neumann-Morgenstern　utility　function,　which　is　a　quadratic　function.　We　will　propose　an　n-asset　portfolio　selection　model　based　on　possibilistic　mean　and　possibilistic　variance　and　discuss　its　optimal　solution.　©　2005　IEEE.