The quasicrystalline structure found in the isothermally aged microstructure in an Al–10Mg–0.5Ag (mass%) alloy after solution treated, water quenched and then aged during the time between 20 and 40 min at 240°C has been characterised using transmission electron microscopy, electron microdiffraction and energy dispersive x-ray spectroscopy. The morphology of the quasicrystalline precipitate particles is rhombohedral in shape and those precipitate particles are homogeneously nucleated, and finely and uniformly dispersed in the matrix. The orientation relationship between the quasicrystalline phase and the α-Al matrix is as follows; i5||⟨011⟩_α and i3||⟨111⟩_α. The quasilattice constant a_R of the icosahedral quasicrystalline phase is estimated to be 0.505±0.01 nm from the present 5-fold electron microdiffraction patterns. The lattice parameter a_c of the corresponding crystalline cubic approximant is thus calculated to be 1.390±0.028 nm. This is in good agreement with the lattice parameter of the crystalline T phase (Mg₃₂(Al,Ag)₄₉, a=1.416 nm). The morphology of the quasicrystalline precipitate particle is consistent with that predicted from the intersection point group \\bar3, which was defined by symmetry elements common to the two lattices in the observed orientation relationship. The quasicrystalline particles contain elements of Al, Mg and Ag. The quasicrystalline precipitate particles, which are the metastable phase, appear to be the primary strengthening phase in the Al–10Mg–0.5Ag (mass%) alloy aged at 240°C.