The existing ultra-fast non-unit protection methods for modular multilevel converter (MMC) HVDC grids based on the protection boundary have shortcomings, such as a lack of adaptive ability and difficulties in threshold setting. The key point is that it is hard to obtain the status of the fault point, which makes the method that uses a fixed threshold value difficult to adapt to various fault conditions. In this paper, the fault voltage which is composed of many sub-components is analyzed based on the built equivalent circuit of MMC-HVDC grids after DC line faults. A fault resistance estimation method is proposed by utilizing the ratio of the second module maximum to the initial module maximum after filtering by a multi-resolution morphological gradient algorithm, and the approximate difference in propagation distance is obtained by using the time difference and the change directions of the initial two surges to correct the influence of distance. A self-adaptation non-unit protection scheme is proposed based on the estimated fault resistance, which consists of the start-up unit, identification of fault types, fault resistance estimation, and self-adaptation main protection. A four-terminal ring-topology MMC-HVDC grid built in PSCAD/EMTDC demonstrates the higher performance of the proposed scheme under various fault conditions.