Voltage source converter-based multi-terminal high-voltage direct current (VSC-MTDC) systems are starting to be commissioned. However, concentrated integration of large-scale wind power demands stronger robustness against power fluctuation and system disturbances to increase the reliability of the whole system. This study proposes a perturbation observer-based robust passivity-based control (PORPC) for VSC-MTDC systems connected to an offshore wind farm to meet the demands. The aggregated effect of system nonlinearities, parameter uncertainties, unmodelled dynamics and external disturbances includes grid faults and time-varying wind power output is estimated by a linear perturbation observer and fully compensated by a passive controller, thus no accurate VSC-MTDC system model is required. PORPC attempts to regulate DC voltage and reactive power at the rectifier side, as well as active power and reactive power at the inverters side connected to an offshore wind farm. Besides, a DC-link voltage droop controller is introduced so as to provide immediate response to the grid unbalance situation. Moreover, a noticeable robustness against parameter uncertainties can be achieved as no accurate system model is needed. Case studies are carried out to compare the performance of PORPC to other typical approaches. Finally, a hardware-in-the-loop test is undertaken via dSPACE which validate its implementation feasibility.