Morphing quadrotors that can be potentially applied to confined spaces such as warehouses, tanks, and pipelines have flourished in recent years. Most work has focused on the mechanical feasibility of the morphing systems and high-level flight controller design, with limited discussions on low-level control. In this paper, a constrained model predictive control (MPC) is proposed and applied to solve the attitude control problem of a morphing quadrotor. Prior to controller design, a custom-built morphing quadrotor is introduced with the kinematic and dynamic models established and corresponding issues and challenges presented. In the controller, to eliminate the steady-state error, an embedded integrator is adopted by exploiting the differential variables; then, the constraints of the morphing quadrotor are incorporated into the MPC formulation to simulate real flight conditions, and an orthonormal function is employed to approximate the control input sequences in the controller to alleviate the computational burden. In the comparative studies, several scenarios are considered to demonstrate the effectiveness of the proposed control strategy in attitude control.