For discrete-time linear parameter-varying (LPV) systems, this paper proposes a new guaranteed cost LPV output-feedback controller to minimize an upper bound of state and input energy called LQ performance under all admissible grades of time-varying parameters. Using the current-time and one-step-past information of the time-varying parameters, this paper designs the new controller associated with a new parameter-dependent quadratic Lyapunov function in terms of parameterized linear matrix inequalities (PLMIs).