The potential application of TiZrNi quasicrystals was evaluated by measuring the pressure-composition-temperature curves after replacing Zr by Pd to the limit maintaining the host structure for the samples made with Ti53Zr27(-x)Ni20Pd(x), where 0 < or = x < or = 8. The results of X-ray diffraction data revealed that the samples keep the pure quasicrystal structure to the maximum value of x = 8. All diffracted peaks uniformly shifted to the low angle of 2 theta in X-ray diffraction pattern suggesting that hydrogen atoms homogeneously diffuse in the quasicrystals and uniformly expand the quasilattice constants without modification of the structure. After hydrogenation at elevated temperature, the quasi-lattice constants increased from 5.12 to 5.34 angstroms for the samples made with x = 0 without appearing an impurity phase. When Zr was replaced by 8 at.% of Pd, the equilibrium vapor pressures significantly increased to 3.41 from 0.41 Torr at 300 degrees C although the total amount of hydrogen decreased as increasing Pd concentration. These results demonstrate that Pd will play a critical role in application for the TiZrNi quasicrystals as hydrogen storage materials.