By using the first-principles DFT calculations, we design a novel hydrogen storage material, Li(12)Si(60)H(60) composite, and validate its geometric stability. It is found that the adsorbed Li atoms do not cluster on the Si(60)H(60) fullerene unlike other metals such as Ti, owing to the relatively low Li-Li binding energy and the inhibition of Si-H bonds. Our results show that the Li-doping enhances the hydrogen adsorption ability of Si(60)H(60) significantly, owing to the charge transfer from the doped Li atoms to the host material and the polarization of the adsorbed H(2) molecules. By combining the first-principles calculation and grand canonical Monte Carlo simulation, we further investigate the hydrogen storage capacity of the simulation-synthesized exohedral Li(12)Si(60)H(60) composite at T = 77 K. As the vdW gap (i.e., the separation between the surfaces of two Li(12)Si(60)H(60) fullerenes) is equal to 8.2 A, the total hydrogen uptake of the square-arranged Li(12)Si(60)H(60) array reaches 12.83 wt % at p = 10 MPa, while the excess hydrogen uptake shows a maximum of 7.46 wt % at p = 6 MPa. Impressively, at T = 298 K and p = 10 MPa, the Li(12)Si(60)H(60) array still exhibits a total hydrogen uptake of 3.88 wt % at the vdW gap of 8.2 A. These results clearly indicate that the composite, Li(12)Si(60)H(60) fullerene, is a promising candidate for hydrogen storage.