This paper studies the problem of the synchronous oscillation caused by Doubly Fed Induction Generator (DFIG) grid connection, and sets up equivalent model of DFIG motor and converter. Based on dynamic equivalent impedance analytic expression, the key factors of grid-connected impedance characteristics are analyzed. The results show that the internal loop gain of the controller rotor side has a large effect on the impedance characteristics of subsynchronous frequency band. On this basis, the paper puts forward a subsynchronous oscillation suppression method based on broadband rotor additional damping control. The proposed method is implemented on converter control of DFIG rotor side, without additional device and good for engineering application. Finally, the validity and applicability under transient condition of the suppression strategy are verified by time-domain simulation.