A new adaptive control method based on high-gain scaling technique is presented for a class of feedforward nonlinear systems with unknown growth rate. With this method, the global stabilization problem of the studied system is solved. Moreover, A key feature of the proposed algorithm is that it employs no parameter estimation. It is shown that all the signals of the closed-loop system are globally bounded and the system states converge to zero asymptotically. A simulation example is provided to demonstrate the effectiveness of the theory.