Cross-streamline migration of a vesicle in a bounded Poiseuille flow is investigated experimentally and numerically. The combined effects of the shear gradient of the flow and of walls induce a migration of the vesicle towards the center-line of the channel. A migration law (as a function of relevant structural and flow parameters) is presented. This similarity law is compared with the laws governing the migration velocity of a vesicle in an unbounded Poiseuille flow and in a shear flow near a wall. The relative contributions of both effects are discussed.