This paper presents a control of the parallel operation of diode rectifier based high-voltage direct current (DR-HVDC) and voltage source converter based HVDC (VSC-HVDC) links. The two links are connected to offshore wind farms (OWFs). The VSC-HVDC controls the voltage and frequency of the offshore AC-grid needed for the OWFs start-up. The proposed grid forming control is based on controlling the OWFs voltage by controlling the active power balance at the VSC-HVDC AC-bus. When the OWFs inject more power than a certain active power reference established for the VSC-HVDC, the OWFs voltage increases and the DR-HVDC starts conducting. Then, the offshore voltage automatically accommodates the required value for transmitting the OWFs power through the DR-HVDC link while the system frequency is controlled by the VSC-HVDC through satisfying the reactive power balance. The power transmitted through the VSC-HVDC can be set by adjusting the corresponding power command while the DR-HVDC will automatically close the power balance. The main advantage of the proposed control system is that the VSC-HVDC can be sized just to support the system energization; while once the OWFs are in operation, the DR-HVDC will be loaded automatically. Simulation results verify the proposed control system.