The orbital manoeuvre of a CubeSat is an essential ability in the process of constellation deployment and other missions. Therefore, an attitude control method based on piece-wise affine (PWA) MPC was proposed for CubeSats during orbital manoeuvres. Then, a solid thruster with high thrust that was previously applied only to large and traditional satellites was innovatively applied to CubeSats for orbital manoeuvres. However, the solid thruster with high thrust has a large eccentric torque from the thrust deviation, so it will cause rapid attitude rolling and result in orbital manoeuvre mission failure. Hence, PWA-MPC strategy with the disturbance observer was designed, which can solve the eccentric torque problem and achieve high accuracy attitude control by a hybrid actuator composed of momentum wheels and a cold gas thruster. In addition, during the orbital manoeuvre process, propellant consumption results in a continuous change in the moment of inertia of a CubeSat. In order to offset this change, the guide rail of the cold gas thruster was innovatively designed to move the cold gas thruster in the working process of the solid thruster. Finally, real-time hardware-in-loop simulation results show that the PWA-MPC strategy has higher attitude stability than those of other MPC strategies in the orbital manoeuvre process of a CubeSat and deserves to be applied.