This paper investigates a finite-time attitude manoeuvre control problem for a flexible spacecraft subject to bounded external disturbances. A robust discontinuous finite-time controller with terminal sliding mode control is designed to solve this problem provided that the disturbances and the coupling effect of flexible modes are bounded with a known boundary. The controller is further enhanced by an adaptive scheme to deal with the more practical case that the boundary is unknown. The enhanced version is continuous and chattering-free. The results are rigorously proved using the Lyapunov stability theory. The effectiveness and robustness of the proposed controllers are demonstrated by numerical simulation.