The objective of this paper is to address the linear state-feedback control problem for a family of high-order uncertain nonlinear systems. Based on the adding a power integrator technique, the authors recursively construct a linear controller with dynamic gains, which can be used to deal with the uncertain nonlinear terms and simplify the controller structure. Moreover, it is proved that the proposed control law can globally regulate system states to the origin and guarantee the boundedness of all the signals of the closed-loop system as well. Finally, a simulation example is presented with some comparison with the existing result so as to demonstrate the effectiveness of the proposed design scheme.