With increasing demand for energy, nuclear fusion has attracted more and more attention. In fusion process, the most promising of fusion reactions is the fusion of deuterium and tritium. Thus, deuterium absorption has become a key issue. At present, the extensively used materials for storage and supply of deuterium are uranium beds. However, upon hydrogenation, uranium is easily disintegrated into fine powder, which causes many undesirable problems. It has been found that zirconium alloys can take as much deuterium atoms as that of uranium alloys but with a lower density and price, thus becoming a candidate material for deuterium carrier. However, zirconium alloys usually occur to crack after deuterium absorption, which badly restricts their application as a deuterium carrier. In order to minimize the cracking, Cu is chosen as an alloying element, expecting to minimize the cracking. In this work, the kinetic mechanisms of deuterium absorption in Zr-xCu (x=0, 5%, 10%, mass fraction) alloys were investigated based on experiments and kinetic function calculations. The results show that with the increase of Cu content, the microstructure transforms from the primary single a-Zr phase of the pure Zr to the a-Zr and Zr₂Cu duplex phases of the Zr-5%Cu and Zr-10%Cu alloys. Correspondingly, the equilibrium time of deuterium absorption increases significantly from 20 min for the pure Zr to 80 min for the Zr-5%Cu alloy and to 130 min for the Zr-10%Cu alloy. After deuterium absorption, the phase of pure Zr is e deuteride while the phases of Zr-5%Cu and Zr-10%Cu are e deuteride, Zr₂Cu and Zr₇Cu₁₀. The kinetic mechanisms of deuterium absorption in these alloys are found to be controlled by a 2-dimensional diffusion mechanism in the pure Zr, and by a chemical reaction mechanism in the Zr-5%Cu and Zr-10%Cu alloys. The addition of Cu changes the kinetic mechanisms of the Zr-xCu alloys, resulting in slowing down deuterium absorption rate. It is attributed that during deuterium absorption of Zr-Cu alloys, Zr₂Cu also absorbs deuterium and forms intermediate phase, such as Zr₂CuH_x. Then the intermediate phase will discompose into Zr₇Cu₁₀ and ε deuteride.