This paper reports on a fault tolerance control (FTC) scheme for a multirotor UAV with actuator faults. The proposed FTC is based on model predictive control, which can be applied to nonlinear systems by using the successive convexification algorithm, which converts a nonconvex function to a convex function in a successive manner through linearization. The faults are parameterized in the form of the loss of effectiveness and estimated through fault detection and diagnosis (FDD). In contrast to the existing FTC schemes, the proposed scheme can control not only small partial losses of the actuator effectiveness, defined as non-severe faults, but also a complete loss of the effectiveness, defined as failure. Furthermore, the proposed FTC can control even severe partial faults that critically impede the normal control of the multirotor, which have not been considered in the existing work. Moreover, the proposed FTC approach does not require controller switching, and the actuator saturation limit is considered. The approach was validated under various actuator fault conditions through nonlinear simulation studies involving two-stage Kalman-filter-based FDD.