The whiskers spontaneously grown in Cd–Mg–Yb alloy containing icosahedral quasicrystal as dominant phase have been investigated by electron microscopy. It is found that: (i) the whiskers are mainly composed of Cd with growth direction along . CdO particles are frequently observed on surfaces of whiskers and the alloy, indicating the importance of the oxidation process during the whisker growth; (ii) there exist four types of orientation relationship between Cd and CdO. The interfaces between them are shown to accommodate large lattice misfit, which is well explained by near coincidence site lattice model; (iii) nanosized Cd particles are observed to aggregate around the whisker root, providing a convincing experimental evidence for the long-range atomic diffusion. Our study offers a unique opportunity to unveil the relationship between unstability of quasicrystal structure and whisker formation and may have some implications for oxidation process of metals.