The conventional linear parameter varying (LPV) modeling for turbofan engines is performed at a set of equilibrium points, which may result in inaccurate description of dynamics of engines when the engine accelerates/decelerates in a broad range and operates away from the equilibria. Meanwhile, to ensure stable operation of turbofan engines, the engine pressure ratio (EPR) needs to be regulated when turning on afterburner. According to this complex multi-input multi-output (MIMO) problem mixed with disturbances, this paper proposes a hybrid robust control framework based on off-equilibrium linearization. We first establish an off-equilibrium linearization based polynomial LPV model for the MIMO turbofan engine, and then design an robust controller by solving sum-of-squares (SOS) programing. The simulation results show that the controller can simultaneously achieve fast dual command tracking and disturbance suppression when turning on afterburner. Furthermore, this control framework is superior to the equilibrium linearization-based controller in many aspects, which further proves the accuracy of the off-equilibrium based LPV model.