In this payer a new model predictive controller (MPC) is developed for polytopic linear parameter varying (LPV) systems. We adopt the paradigm used in gain scheduling and assume that the time-varying parameters are measured on-line, but their future behavior is uncertain and contained in a given polytope. At each sampling time optimal control action is computed by minimizing the upper bound on the "quasi-worst-case" value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs. The MPC algorithm is called "quasi" because the first stage cost can be computed without any uncertainty. This allows the inclusion of the first move u(k\k) separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints. Proposed optimization problems are solved by semi-definite programming involving linear matrix inequalities. It is shown that closed-loop stability is guaranteed by the feasibility of the linear matrix inequalities. A numerical example demonstrates the unique features of the MPC design.