In this paper, a combination of dynamic constrained control allocation with terminal sliding mode control is proposed for a general class of overactuated nonlinear systems with actuator faults/failures. First, the terminal sliding mode control is designed to converge the system tracking error to zero in a finite-time. Then a control allocation strategy is developed and will be solved by a Lyapunov method, which leads to a dynamic update law with finite-time convergence. This strategy satisfies input limits and when faults/failures occur in some of the actuators, the control signals are automatically redistributed among the healthy actuators. Simulation results on a near space vehicle show the effectiveness of the proposed approach.