Based on adaptive nonlinear damping, a robust adaptive output feedback controller is proposed for a multi-input and multi-output nonlinear system with unknown nonlinear parameters, uncertain nonlinearities, bounded disturbance, unmodeled dynamics and uncertain control parameters. It is proved that all the signals in the closed-loop are bounded and the control errors and estimation errors can be made arbitrarily small by choosing some design parameters appropriately. The controller only has an adaptive control parameter and an adaptive observer parameter no matter how high the order of the system is and how many unknown parameters there are. Simulation results show the effectiveness of the proposed controller.