In this study, a novel output feedback model predictive control based on ellipsoidal set-membership state estimation is proposed for systems with unknown but bounded external disturbances. The set-membership state estimation is utilised to estimate the current system states for the optimisation of model predictive control such that the actual states are not required. Ellipsoidal set-membership estimation guarantees that the real system state lies in the ellipsoid originated from the estimated state. The control inputs computed by solving the optimisation problem recursively regulate the system state to converge to a domain containing the origin. All the quadratic matrix inequality conditions are conservatively approximated as linear matrix inequality conditions such that the optimisation problems can be solved by using semi-definite programming. System constraints are analysed over all the prediction horizon and transformed into linear matrix inequalities for the direct incorporation into the optimisation. Simulation examples demonstrate the effectiveness of the proposed approach.