This note considers the problem of global stabilization for a class of feedforward systems whose nonlinearities are allowed to be lower-order growing, instead of higher-order or linear growing as required by many existing results. To solve the problem, a domination approach is developed to design the stabilizer with a new structure, which is also integrated with the adding a power integrator and nested saturation methods. The use of a locally homogeneous stabilizer enables us to relax the growth condition imposed on the nonlinearities and hence enlarges the class of feedforward systems which are globally stabilizable.