Multi-terminal VSC-HVDC transmission is a promising solution to transport energy from the generating plants to the distribution stations, and the number and size of the corresponding power grids is expected to increase in the next years. Such a system presents challenging control problems that, so far, have been approached with classical control techniques. However, large scale systems of interconnected nodes fall within the framework of the emerging field of complex networks. This paper analyzes the stability of multi-terminal VSC-HVDC systems from a complex dynamical network perspective, and provides sufficient conditions to ensure bounded synchronization of its trajectories. The obtained results are validated via numerical simulations.