Field experiences have shown that sub-synchronous oscillations (SSOs) can occur in direct-drive wind farms with VSC-HVDC (DDWFV) systems. In light of this, a dynamic mathematical model of the DDWFV is established in this Project. The SSO characteristics are analysed through the eigenvalue method. Considering the participation factor, the analysis reveals that the SSO is mainly affected by the grid-side converter controller of the wind turbine units, the rectifier controller of the VSC-HVDC and certain system parameters. The impact of system parameters on the damping performance and frequency characteristics of the SSO is further explored. By separating the VSC-HVDC into three parts, the impact of the control characteristics and the AC-side elements characteristics of the VSC-HVDC on the SSO is discussed. New insights into the SSO issue are also offered by analyzing the interaction among various state variables. The theoretical analysis is verified by extensive time-domain simulations.