The rapid internal-fault identification capability of an VSC-MTDC is of great significance for the safety and stability of a power system. At present, DC line differential protection does not take the capacitive current into consideration, and the lack of speed makes it suitable only as a back-up protection. To solve this problem, a novel DC line differential current protection with high sensitivity is proposed. This can identify internal faults within a very short time window. First, the capacitive current is fully compensated based on the Bergeron model. Secondly, an adaptive threshold is set against the high sensitivity of the proposed method to the parameters of the system. Finally, based on the difference of Hausdorff distance between the original measurement and the deduced measurement, a novel DC current differential protection adaptive to the characteristics of the VSC-MTDC is put forward. Theoretical analysis and simulation results indicate that the proposed protection can identify internal fault sensitively and reliably, and the speed is high enough to meet the requirements for fault-isolation of VSC-MTDC systems. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. 5100-201999331A-0-0-00) and National Natural Science Foundation of China (No. 51907069).