This　paper　discusses　the　portfolio　selection　problem　with　the　lower　and　upper　bounds　constraints　to　investment　based　on　the　possibilistic　theory　under　the　assumption　that　the　returns　of　assets　are　fuzzy　numbers.　The　possibilistic　mean　value　of　the　return　is　termed　measure　of　investment　return　and　the　possibilistic　variance　of　the　return　is　termed　measure　of　investment　risk.　The　conventional　probabilistic　mean-variance　model　can　be　simplified　a　linear　programming　under　the　assumption　that　the　returns　of　assets　are　triangular　fuzzy　numbers.　Finally,　a　numerical　example　of　a　portfolio　selection　problem　is　given　to　illustrate　our　proposed　effective　means　and　approaches.