Protection against dc faults is one of the main technical challenges for the operation of converter-based HVdc systems. Protection becomes even more challenging when the HVdc systems are expanded to multi-terminal dc (MTdc) grids with more than two terminals/converter stations. Similar to their ac counterparts, proper protection of the MTdc grids necessitates both primary and backup protection schemes in which, in case of malfunctioning/failure of primary protection, backup protection trips as fast as possible. Although several backup relaying algorithms, such as current threshold- and classifier-based methods, have been proposed, none of them offers sufficient speed, robustness, and scalability. In this paper, a novel backup protection algorithm based on quickest change detection technique is proposed, which offers fast and robust backup protection functionality for the primary relay. The performance and effectiveness of the proposed algorithm are evaluated and verified with time-domain simulation studies in the PSCAD/EMTDC environment. The study results confirm satisfactory performance of the proposed algorithm in terms of accuracy, robustness, and speed under various fault scenarios. The proposed method is applicable to different grid configurations and is able to cooperate with different primary protection algorithms and breaker configurations.