In this work, a decentralized PI passivity-based controller (PI-PBC) is applied to Modular Multilevel Converters (MMCs) to ensure global stability of a multi-terminal HVDC system. For the derivation of the controller, an appropriate model with constant steady-state solutions is obtained via a multi-frequency orthogonal coordinates transformation. The control design is next completed using passivity arguments and performance guarantees are established by a small-signal analysis. The obtained results are validated by means of detailed time-domain simulations both on a single-terminal and a four-terminal benchmark.