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The system of offshore direct-drive wind farm connected to the power grid via voltage source converter based high voltage direct current (VSC-HVDC) transmission consists of several converters, which have different time scale control loops and complex dynamic characteristics. Based on an example case with two direct-drive wind farms and VSC-HVDC transmission system, the sub/super-synchronous oscillation modes of the system and its relationship with current control loops are studied by state space analysis. The research shows that there are three dominant modes related to the current control of the converter in the system, which are the oscillation mode between wind farms and the offshore converter station, the mode between the offshore wind farms, and the mode between the onshore converter station and the alternating current (AC) system. The modes at the wind farm side are decoupled from the mode between the onshore converter station and the AC system. The relevant control parameters of the converters and the operating conditions have an important impact on the stability of the three modes. The oscillation caused by the single dominant mode may spread to the other side of VSC-HVDC, which means it is necessary to identify the root cause of oscillation in order to design the suppression strategy. The research results is of guidance to the understanding of the dynamic characteristics of offshore wind power grid-connected systems via VSC-HVDC, parameter design, and oscillation suppression.