Based on Moore and Greitzer's model [15], the surge behavior of axial flow compression system was found to be attributed to the appearance of Andronov-Hopf bifurcationin [12]. In this paper, we focus on the design of control law to prevent and/or delay the occurrence of the bifurcations, which will then suppress the surge behavior. Both types of linear dynamic state feedback and linear washout filter controllers are proposed. The proposed washout design does not require the explicit knowledge of the operating point and keep the original equilibrium characteristic while the dynamic feedback design will change the equilibrium operating points for pre-surge and post-surge regime. In addition, the washout type control scheme can relax the implementation of the control law in the practical applications. Numerical results demonstrate the effectiveness of the proposed designs and the superiority of the washout filter scheme.