To address the issue that conventional quadrotor UAVs have limited movement modes and the rotor thrust direction is fixed relative to the body, this paper considers a class of quadrotor UAVs with tilt rotors, which could change their shape and structure according to the needs of the flight environment and mission, thus providing better control capabilities and wider applications. In view of the nonlinear characteristics and complex dynamic model of this kind of UAVs, using the Jacobian linearization method to build a corresponding linear parameter varying (LPV) model. In accordance with the Lyapunov quadratic stability theory and the linear matrix inequality (LMI) method, a gain scheduling state feedback controller solution method is derived for the LPV model to cope with changing flight environment and mission requirements. The effectiveness of the proposed controller for the quadrotor UAV with tilt rotors is verified through numerical simulations.