The invention relates to a nanocrystalline amorphous Mg-M-Y hydrogen storage alloy and a preparation method thereof. Specifically, the nanocrystalline amorphous magnesium-based hydrogen storage alloy is composed of three components, by weight, of 65-87% of Mg, 2-15% of Y and 4-23% of M; and the M is one of aluminum (Al), nickel (Ni), iron (Fe), cobalt (Co), manganese (Mn), vanadium (V), chromium (Cr), copper (Cu) or titanium (Ti). The preparation method of the nanocrystalline amorphous Mg-M-Y hydrogen storage alloy is that the nanocrystalline amorphous Mg-M-Y hydrogen storage alloy is directly obtained by adopting reaction ball mill under the hydrogen atmosphere. The process route is shortened, the material preparation efficiency is greatly improved, and by adoption of the obtained nanocrystalline amorphous Mg-M-Y alloy, the high hydrogen absorption and desorption speed rate and the hydrogen storage amount are achieved without activation.