The dynamics of the forced vibration and its delayed feedback control of a gyroscope system are investigated in this paper,. The differential equations of motion with two degrees of freedom are obtained based on the Lagrange equation. For the case of primary resonance and 1:1 internal resonance, the averaging method is used to derive the averaged equations. Then according to the theory of singularity, the bifurcation equation acquired from the averaged equations, is simplified to analysis the bifurcation behavior of the system. Finally, the effects of feedback parameters on the amplitude of the forced vibration are discussed for the linear position and velocity feedback control with time delay.