Under weak grid conditions, oscillation in wind power integrated system occurs frequently. However, existing oscillation suppression methods face challenges in effectively coordinating control parameters and fail to guarantee excellent dynamic performance. Therefore, this paper proposes an uncertainty and disturbance estimator-based feedback linearization sliding mode control (UDE-FLSMC) method, which can reduce the negative damping region of the impedance phase of wind power integrated system. Firstly, the feedback linearization process of multi-input multi-output (MIMO) systems is derived. Then, the uncertainty and disturbance estimator (UDE) is used to estimate the disturbance in sliding mode control, and the UDE-FLSMC method is proposed. Secondly, the control structure and impedance model of wind power grid-side converter (GSC) are established. The impact of control parameters on the impedance characteristics of the converter is analyzed. It is demonstrated that the impedance phase in sub/supersynchronous frequency band maintains within a significant positive damping region under different operating conditions. Then, a hardware-in-loop experimental platform is constructed to verify the dynamic performance of the proposed UDE-FLSMC method, which is compared with proportional integral (PI) control and phase margin frequency division compensation (PM-FDC) control. The results show that the proposed UDE-FLSMC method exhibits superior oscillation suppression ability and faster response characteristics, which can significantly improve the stability of wind power integrated system under weak grid conditions.