Precipitation of the ordered icosahedral quasicrystal in Mg-6wt%Zn-1wt%Y alloy has been characterized bytransmission electron microscopy observations. The lamellar-type icosahedral qusicrystal phases (I-phase) with the face-centeredicosahedral (FCI) structure are observed in alloy after solution treatment at 550oC. In the alloy annealed at 400oC, polygon-shaped I-phases are observed in the α-Mg matrix. The interfaces of the I-phase with the matrix are facetted and the facets areon five-fold and two- fold plane of the I-phase. The orientation relationship of the I-phase with the matrix is determined tobe [I5]I//[001]Mg, (2f)I//()Mg and [I2]I//[311]Mg, (5f)I//()Mg. The icosahedral grains are occasionally found to be twinnedwith one of the five-fold axis as the twin axis. The twin boundaries appear to be fairly straight and perpendicular to the five-fold twin axis. The icosahedral twin can be expressed as a rotation of 63.4o or 116.6o around two fold zone axis.