Snow depth on the interior of Tibetan Plateau (TP) in state-of-the-art reanalysis products is almost an order of magnitude higher than observed. This huge bias stems primarily from excessive snowfall, but inappropriate process representation of shallow snow also causes excessive snow depth and snow cover. This study investigated the issue with respect to the parameterization of fresh snow albedo. The characteristics of TP snowfall were investigated using ground truth data. Snow in the interior of the TP is usually only some centimeters in depth. The albedo of fresh snow depends on snow depth, and is frequently less than 0.4. Such low albedo values contrast with the high values (~0.8) used in the existing snow schemes of land surface models. The SNICAR radiative transfer model can reproduce the observations that fresh shallow snow has a low albedo value, based on which a fresh snow albedo scheme was derived in this study. Finally, the impact of the fresh snow albedo on snow ablation was examined at 45 meteorological stations on TP using the land surface model Noah-MP which incorporated the new scheme. Allowing albedo to change with snow depth can produce quite realistic snow depths compared with observations. In contrast, the typically assumed fresh snow albedo of 0.82 leads to too large snow depths in the snow ablation period averaged across 45 stations. The shallow snow transparency impact on snow ablation is therefore particularly important in the TP interior, where snow is rather thin and radiation is strong.