Hydrogen is a clean, abundant, no-toxic, renewable fuel and packs more energy per unit mass than others. It is important to find a efficient way to store it. Hydrogen molecules adsorbed on the Al doped BN sheets are investigated by using density function theory (DFT) calculations. The results indicate that the H2 molecule is very easy to be absorbed on the doped BN sheet of B substituted by an Al atom (AlB-BN), which is most stable structure in all the Al doped configurations. Therefore, AlB-BN is a promising material in storage H2.