The adsorption of multiple hydrogen molecules on two different types of heptazine-based graphitic carbon nitride nanotubes (hg‒C3N4‒NTs), namely armchair (3,3) and zigzag (6,0) hg‒C3N4‒NTs, decorated with Al atom, was investigated using the periodic DFT method. The first hydrogen molecule adsorbed on all outer surfaces of Al-decorated hg‒C3N4‒NTs was found to be a dissociative H2 chemisorption and exhibited significantly stronger interaction than subsequent hydrogen molecules (the second to fourth). Notably, the first hydrogen molecule adsorbed on Al-decorated on armchair (3,3) and zigzag (6,0) hg‒C3N4‒NTs demonstrated high potential for hydrogen storage, with the strongest chemisorption observed on Al-decorated zigzag (6,0) hg‒C3N4‒NT, which exhibited an adsorption energy of -1.89 eV. Furthermore, the corresponding pristine armchair (3,3) and zigzag (6,0) hg‒C3N4‒NTs can serve as representative molecular models for the hg‒C3N4‒NTs.