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This paper presents a new parameter-scheduled controller design and solving method for turbofan engine polynomial linear parameter varying (PLPV) model in nonconvex domain. In this method, the parameterized linear matrix inequalities (PLMI)-typed sufficient conditions based on parameterized Lyapunov function (PLF) are given, which can guarantee multi-objective robust performances of the control system. Then, by using the geometrical features of parameter domain, an improved convex polyhedron construction algorithm is proposed. Based on this improved algorithm, the parameter-scheduled controller solving problem is reduced into a linear matrix inequalities (LMI) constrained normal convex optimization problem. The numerical simulations on a turbofan engine verify the effectiveness of the controller design and satisfactory global control performance.