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Ti-Zr-Ni-based icosahedral quasicrystals (IQCs) are a type of hydrogen storage materials with promising application in the fields of hydrogen energy and nuclear fusion energy. In the present paper, the preparation of Ti39Zr38Ni17Pd6 IQC and its deuterium storage properties were investigated by XRD, TEM, XPS analysis and a gas-solid reaction system. Results show that the saturation concentration of absorbing deuterium for the alloy at room temperature reaches near 11 mmol·D2/g·M (D2 means deuterium molecular and M the metal), exceeding those of Zr2Fe and ZrCo alloys. After a few absorption/desorption cycles, no phase transformation is observed, but the quasilattice displays a remarkable expansion of 6.37% after full D intake. The binding energy rise of 0.2 eV for Ti and 0.6 eV for Zr, caused by the introduction of saturated deuterium atoms, provides the evidence of the preferential location of deuterium near Zr and Ti in quasicrystals of this kind. The possible existence of a lower D desorption equilibrium pressure with <1 kPa at about 350 °C reflects higher thermodynamic stability of deuterium in the IQC than in ZrCo alloy. The advantages in hydrogen volume, thermal and structural stabilities suggest that the quasicrystals of this type could be a candidate to replace Zr2Fe and ZrCo in nuclear fusion field.