The over-current capacity of half-bridge modular multi-level converter (MMC) is quite weak, which requests protections to detect faults accurately and reliably in several milliseconds after DC faults. The sensitivity and reliability of the existing schemes are vulnerable to high resistance and data errors. To improve the insufficiencies, this paper proposes a pilot protection scheme by using the random matrix for DC lines in the symmetrical bipolar MMC high-voltage direct current (HVDC) grid. Firstly, the 1-mode voltage time-domain characteristics of the line end, DC bus, and adjacent line end are analyzed by the inverse Laplace transform to find indicators of fault direction. To combine the actual model with the data-driven method, the methods to construct the data expansion matrix and to calculate additional noise are proposed. Then, the mean spectral radiuses of two random matrices are used to detect fault directions, and a novel pilot protection criterion is proposed. The protection scheme only needs to transmit logic signals, decreasing the communication burden. It performs well in high-resistance faults, abnormal data errors, measurement errors, parameters errors, and different topology conditions. Numerous simulations in PSCAD/EMTDC confirm the effectiveness and reliability of the proposed protection scheme.