The　paper　aims　to　investigate　the　unsteady　natural　convection　flow　and　heat　transfer　of　fractional　Maxwell　viscoelastic　nanofluid　in　magnetic　field　over　a　vertical　plate.　The　effect　of　nanoparticle　shape　is　first　introduced　to　the　study　of　fractional　Maxwell　viscoelastic　nanofluid.　Fractional　shear　stress　and　Cattaneo　heat　flux　model　are　applied　to　construct　the　governing　boundary　layer　equations　of　momentum　and　energy,　which　are　solved　numerically.　The　quantities　of　physical　interest　are　graphically　presented　and　discussed　in　detail.　It　is　found　that　particle　shape　and　fractional　derivative　parameters　have　profound　influence　on　the　flow　and　heat　transfer.　©　2018　The　Physical　Society　of　the　Republic　of　China　(Taiwan)