In this paper, we have performed systematic theoretical surveys of C20 and its C20-2nTinNn nanocages with n = 1-8 at DFT. Full optimization indicates none of the structures collapse to open deformed as segregated heterofullerene. Also, in order to avoid the resulted strain of fused five-pentagon configuration, some of them deform their cage at the Ti-N bonds and appear cubic-like. Binding energy (Eb) increases, and the absolute heat of atomization │ΔHat│ of the designed C20-2nTinNn structures decreases, respectively, as the number of substituting Ti-N units increases. The calculated Eb of 57.05eV/atom and │ΔHat│ of 2437.40kcal/mol display C4Ti8N8 as the most thermodynamic stable heterofullerene where including eight separated Ti-N units through two double C═C bonds. In contrast, the calculated band gap of 2.06eV shows C18Ti1N1 as the best-insulated heterofullerene. Here isolable or extractable open-shell C18Ti1N1 heterofullerene must be kinetic stable species, and closed-shell C4Ti8N8 should be thermodynamic stable species. Compared to the suggested Ti-decorated B38 fullerene as a high capacity hydrogen storage material with large Eb (5.67eV/atom), our studied C20-2nTinNn heterofullerenes show the higher Eb with a range of 13.78 to 57.05eV/atom, the higher stability, and the higher capacity hydrogen storage. Each Ti-N unit can bind up to two hydrogen molecules with an average adsorption energy of 0.073eV/H2. While the C4Ti8N8 fullerene substituted with 8 Ti-N units can store 16 H2 molecules, the hydrogen gravimetric density (the hydrogen storage capacity) reaches up to 5.61 wt% with an average adsorption energy of 0.587eV/H2. Based on these results, we infer that C4Ti8N8 fullerene is a potential material for hydrogen storage with high capacity and might motivate active experimental efforts in designing hydrogen storage media.