At present， the start-up of HVDC has not been considered at the initial stage of black-start in China. How to build the models of the AC system and HVDC with PSCAD/EMTDC is introduced， and then the start mode and start-up conditions of the HVDC in the initial stage of black-start are studied by the models. Two indices to measure the intensity of the AC system are proposed as the absolute short-circuit capacity and effective inertia constant. The HVDC can start-up in the monopolar constant current control starting mode with 70% voltage drop when both sides of the AC system can meet the two conditions whereas the absolute short-circuit capacity is about 14 times of one filter capacity and the effective inertia constant of the whole system ranges from 70 s to 90 s. With these conditions satisfied， the HVDC can start-up successfully and the impact to the AC system is minimal.