This paper presents a nonlinear control strategy based on dynamic feedback linearization control theory and a backstepping-like procedure for a multi-terminal voltage-source converter based high-voltage direct current (multi-terminal VSC-HVDC) system. The controller is able to provide asymptotic stability for the power transmission system with multiple terminals. In particular, it is shown that the zero dynamics (mostly representing the DC network) is exponentially stable. These results are obtained by a stability proof for the whole system under the proposed controller, and its performance is illustrated by computer simulations.