The recently proposed power-synchronization control for grid-connected voltage-source converters (VSCs) has been shown to be a feasible solution for high-voltage dc (HVDC) transmission connected to high-impedance weak ac systems. In this paper, power-synchronization control is investigated for VSC-HVDC connected to another type of weak ac system, i.e., low-inertia or island systems. As an example, a linear model of a typical island system feeding by a VSC-HVDC link, including a synchronous generator, an induction motor and some passive loads, is developed for tuning the control parameters of the VSCHVDC. Time simulations in PSCAD/EMTDC demonstrate that VSC-HVDC using power-synchronization control is flexible for various network conditions, such as large-ac-system connection, island systems, or passive networks. The time simulations also show that power-synchronization control can seamlessly handle transitions between the operation modes, as well as ride through ac-system faults in all network conditions.