This paper presents a new adaptive multivariable attitude control method for the reusable launch vehicle (RLV) to track desired attitude trajectories subject to unknown external disturbances and uncertainties. In contrast to most designs neglecting mismatched disturbances, this method employs an adaptive finite-time observer (AFO) to estimate the unknown states. Based on the outputs from the AFO and the prescribed performance function, a time-varying non-overestimated adaptive gain is designed to construct the adaptive multivariable attitude control for the RLV system. Simulation studies were carried out and the results show that the proposed approach is able to steer the RLV to track desired attitude signals in the presence of unmatched disturbances and uncertainties.