Glacier centerlines are fundamental to glacier inventory, ice-flow dynamic modeling, and thickness estimation. Although numerous approaches exist for extracting glacier centerlines, they often involve complex processes, require excessive parameters, and produce noticeable deviations, particularly in the accumulation zones of larger glaciers leading to significant discrepancies in subsequent glacier dynamic modeling and thickness estimation. To address this issue, we propose a novel method that extracts glacier centerlines using only a DEM and glacier outlines as input. Our approach integrates contour gradient derived ridge lines and steep terrain constraints to effectively regulate flow direction, while also incorporating a cost grid and hydrological flow routing for enhanced centerline delineation. This approach is characterized by its fully automatic nature, algorithmic simplicity, and high computational efficiency. A total of 134,790 glacier centerlines were derived across High Mountain Asia using our proposed algorithm. Our approach proves effective in extracting centerlines for individual valley glaciers without manual intervention with robust performance even in rugged terrain. The average glacier length is 1.072 km. In total, 607 glaciers in HMA exceed 10 km, and 6 extend beyond 50 km. The longest centerline extracted in our dataset is 82.371 km, corresponding to Siachen Glacier in the Karakoram. We found the centerlines have a good consistency with glacier velocity, indicating it can represent real flow path for glaciers. Our centerlines extraction approach may be beneficial for glacier conceptual models.