A kind of prescribed performance based adaptive attitude tracking control scheme is discussed for flexible spacecraft attitude tracking problem with external disturbances and unmodeled dynamics. The prescribed performance method utilizes performance functions and error transformation for constraining the system tracking error within prespecified bounds to ensure desired overshoot, convergence rate, and steady-state error. Radial basis function (RBF) neural network is used to deal with the unknown dynamics caused by disturbances and flexible vibration. When considering the existence of the unknown neural network approximation error, the upper bound of the approximation error is further estimated to reduce the conservativeness in parameter selection. By using the designed adaptive laws, the prescribed performance adaptive attitude tracking control law is constructed. A simulation study on a flexible spacecraft system shows that the proposed method can compensate the influence of disturbances and flexible appendages while obtaining a fast transient process and expected attitude tracking accuracy. Compared with the method without using prescribed performance, the proposed method has obvious advantages in the convergence, tracking accuracy, and vibration suppression with lower dependence on control parameters.