In this article, the control problem of rigid-body attitude under constant disturbances without angular-velocity measurement is solved by the combination of the immersion and invariance methodology and the dynamic scaling technique. Two observers, which are respectively for estimating the angular velocity and the disturbance, are constructed by utilising the immersion and invariance method. The mismatched term arising from the observers is dominated by the high-gain injection. The control law is a simple proportional-derivative controller plus a disturbance compensation term, where the estimates of the angular velocity and the disturbance from observers are used for feedback directly. The overall closed-loop system is shown to be almost globally asymptotically stable under easy choices of some control parameters. Finally, simulations are conducted to demonstrate the effectiveness of the proposed control scheme.