This work studies a difficult problem of rigid satellite attitude tracking control without angular velocity measurements. A new output feedback controller is presented by using attitude measurements only. The closed-loop tracking system is ensured to be asymptotically stable. The key feature of this approach is that in comparison with the conventional attitude output feedback control schemes by using angular velocity observers in the existing literature, any observer to estimate the unmeasured angular velocity is not required. The effectiveness of the developed approach is validated by a rigid satellite example with simulation results presented.