When sub-synchronous oscillations (SSO) occur in power grid, they can affect control performance of grid-side converter (GSC) for direct-drive permanent magnet synchronous generators (D-PMSG), thereby impacting overall stability of system. To address this issue, this paper proposes a suppression strategy for SSO based on adaptive notch filter (ANF). Firstly, the mechanism by which grid SSO affects GSC control of D-PMSG based on virtual synchronous generator (VSG) is analyzed, and disturbance propagation path of SSO component is delineated. Secondly, to overcome problem that fixed-parameter notch filters are unsuitable for time varying characteristics of SSO frequencies, an improved fast Fourier transform-based algorithm for identifying SSO parameters is proposed. Based on identification results, a strategy for updating center frequency of ANF is designed. Optimal intervention point of ANF in control system is determined. Finally, by constructing a simulation model, the effectiveness of proposed control strategy for suppressing SSO is verified.