With continuous expansion of capacity and scale of new power systems, series supplementary capacitors are often adopted to improve transmission capacity of lines, but aggravate the risk of sub-synchronous oscillation (SSO) in the power system. SSO will cause voltage oscillation of the doubly-fed induction generator (DFIG) DC bus through the grid side converter (GSC), which will affect control performance of the rotor side converter (RSC), thus leading to power oscillation of the whole power generation system. Therefore, in order to solve the problem of SSO's disturbance to DC bus voltage, this paper brings forward a GSC backstepping SSO suppression strategy based on frequency self-adaptive control. First, the GSC mathematical model under SSO is established, and key factors influencing the DC bus voltage and oscillation suppression strategy of SSO are explored. Then, based on principle analysis of backstepping design and frequency self-adaptive control, the steady-state wave component and SSO component of DFIG DC bus voltage are adjusted respectively, by backstepping controller and frequency self-adaptive controller, to avoid interference of power grid SSO on GSC control. Finally, a simulation model and an experimental platform are built to prove reliability of the proposed theory in this paper and corresponding control strategy. Simulation and experimental results indicate the proposed control strategy can effectively restrain voltage fluctuation of DC bus in GSC under the influence of SSO.