The protection of half-bridge modular multilevel converter-based (MMC) HVDC grids demands balancing selectivity, sensitivity, and robustness while ensuring fast operation. However, existing single-ended protection schemes often struggle with balancing selectivity and sensitivity, while double-ended schemes face challenges in achieving both speed and sensitivity. This study investigates the theoretical characteristics of first fault current traveling waves (FFCTWs) as they propagate along the faulted and non-faulted lines within a grid. Theoretical analysis reveals unique mode-1 FFCTW characteristics at faulted line ends over that of non-faulted ones, overcoming the shortcomings in methods based on the similarity of FFCTWs in ring grids. Protection criteria implementation utilizes directional morphological features of mode-1 currents at the line ends and of local poles’ currents for fault discrimination and classification, respectively. The proposed method avoids certain conditions like strong boundary features or line parameters to be applicable and can operate effectively even under measurement anomalies. To validate the proposed protection scheme, a meshed MMCHVDC grid is modeled using the PSCAD software. Simulation studies verify the selectivity and sensitivity of the scheme in case of various types of low and high-impedance faults, as well as robustness against non-fault operating conditions. Moreover, the applicability of the proposed method is assessed as primary protection and in comparison to state-of-the-art protection methods.