New materials for hydrogen storage of Li-doped fullerene (C20, C28, C36, C50, C60, C70)-intercalated hexagonal boron nitrogen (h-BN) frameworks were designed by using density functional theory (DFT) calculations. First-principles molecular dynamics (MD) simulations showed that the structures of the Cn-BN (n = 20, 28, 36, 50, 60, and 70) frameworks were stable at room temperature. The interlayer distance of the h-BN layers was expanded to 9.96–13.59 Å by the intercalated fullerenes. The hydrogen storage capacities of these three-dimensional (3D) frameworks were studied using grand canonical Monte Carlo (GCMC) simulations. The GCMC results revealed that at 77 K and 100 bar (10 MPa), the C50-BN framework exhibited the highest gravimetric hydrogen uptake of 6.86 wt% and volumetric hydrogen uptake of 58.01 g/L. Thus, the hydrogen uptake of the Li-doped Cn-intercalated h-BN frameworks was nearly double that of the non-doped framework at room temperature. Furthermore, the isosteric heats of adsorption were in the range of 10–21 kJ/mol, values that are suitable for adsorbing/desorbing the hydrogen molecules at room temperature. At 193 K (–80 °C) and 100 bar for the Li-doped C50-BN framework, the gravimetric and volumetric uptakes of H2 reached 3.72 wt% and 30.08 g/L, respectively.