HVDC based on diode-rectifier-unit (DRU-HVDC) provides a possibility to reduce the cost of offshore wind power transmission significantly. When such a technology is adopted, the control strategy of the offshore wind turbine line-side converter (WT LSC) is extremely important for the reliable operation of the system. This paper proposes an innovative WT LSC self-synchronization control comprising the active power control loop, the reactive power control loop, the inner current control loop, the frequency control loop, and the phase-locked loop. The proposed self-synchronization control removes the voltage control loop, which is different from previously-reported grid-forming control of offshore WT LSC, based on the fact that the AC voltage magnitude of DRU is automatically clamped when wind power is transmitted through the HVDC link. Such a control solution leads to less tuning of the control parameter and reduced complexity of control. To optimize control parameters, a small signal stability analysis is conducted. Finally, time domain simulations are carried out in PSCAD platform, and results demonstrate the effectiveness of the proposed self-synchronization control under start-up and offshore AC fault.