In this paper, we design a robust adaptive controller for a flexible spacecraft model. Specifically, the proposed framework involves a new and novel controller architecture involving a modification term in the update law that minimizes an error criterion involving the distance between the weighted regressor vector and the weighted system error states. This modification term allows for fast adaptation without hindering system robustness. In particular, the governing tracking closed-loop system error equation approximates a Hurwitz linear time-invariant dynamical system with L∞ input-output signals with the proposed modification term. This key feature of our framework allows for robust stability analysis of the proposed adaptive control law using L1 system theory. We further show that by properly choosing the design parameters in the modification term we can guarantee a de- sired bandwidth of the adaptive controller, guaranteed transient closed-loop performance, and an a priori characterization of the size of the ultimate bound of the closed-loop system trajectories. A numerical illustrative study is provided to demonstrate the effcacy of the proposed design for a flexible spacecraft model in the presence of system uncertainties and exogenous disturbances.