For direct-drive permanent magnetic synchronous generators (D-PMSGs) grid-connected system, two different sub-synchronous oscillation modes with distinctive characteristics are analyzed by eigenvalue analysis. The dominant link and key influencing factors of each oscillation mode are revealed. Firstly, a linearized small-signal model of the D-PMSGs grid-connected system is established and compared with the detailed model in the PSCAD/EMTD to verify its accuracy. Secondly, by analyzing the eigenvalues of the small-signal model, two types of sub-synchronous oscillation modes with different characteristics are obtained. Furthermore, the root locus method is used to investigate the effect of parameter changes on two types of oscillation modes according to the link which is closely related to the oscillation mode determined by the participation factor. It is found that the excitation of the high-frequency mode depends on the DC voltage control and DC link, while the low-frequency mode is closely related to the grid strength and the phase-locked loop. Finally, the correctness of the analysis including two types of sub-synchronous oscillation characteristics is validated through time-domain simulation. This research provides a reference for recognizing the dynamic characteristics and tuning the inverter control parameters of D-PMSGs grid-connected system.