The Hopf bifurcation characteristic in a relative-rotation dynamical system with nonlinear damping force is analyzed and the necessary and sufficient condition of Hopf bifurcation is given under which the system has Hopf bifurcation emerging from the equilibrium. In order to make the Hopf bifurcation point transformed and control the stability and amplitude of limit cycle，a nonlinear feedback controller is proposed. The analytical results on controlling Hopf bifurcation points via the nonlinear controller agree well with the numerical results.