In this note, we solve the global adaptive stabilization problem for a class of feedforward nonlinear systems which possesses a much more general feedforward structure than those feedforward nonlinear systems which can be globally adaptively stabilized previously. The design of our adaptive stabilizer takes a two-step procedure: we first design a stabilizer containing a certain tuning parameter and then design a switching logic to tune it online in a switching manner. Global stability results of the closed-loop system have been proved, and a simulation example is given.