Adaptive tracking control problem for disturbed nonlinear systems with the time derivative of disturbance being unbounded is investigated in this paper. Different from the existing literatures, a new disturbance observer is constructively proposed with its parameters being functions rather than constants, which results in a new manner for our disturbance observer. The convergence of the new disturbance observer is then proved based on Lyapunov stability theorem. Moreover, it is proved that the tracking error of system can be regulated to arbitrary small by appropriately choosing the design functions and parameters. Finally, simulation results are given to demonstrate the effectiveness of designed method.