Precipitation of the ordered icosahedral quasicrystal in Mg-6wt%Zn-1wt%Y alloy has been characterized by transmission electron microscopy observations. The lamellar-type icosahedral qusicrystal phases (I-phase) with the face-centered icosahedral (FCI) structure are observed in alloy after solution treatment at $550^{circ}C$. In the alloy annealed at $400^{circ}C$, polygon-shaped I-phases are observed in the ${alpha}$-Mg matrix. The interfaces of the I-phase with the matrix are facetted and the facets are on five-fold and two- fold plane of the I-phase. The orientation relationship of the I-phase with the matrix is determined to be $[I5]_I//[001]_{Mg}$, $(2f)_I//(2overline{1}0)_{Mg}$ and $[I2]_I//[311]_{Mg}$, $(5f)_I//(0overline{1}1)_{Mg}$. The icosahedral grains are occasionally found to be twinned with one of the five-fold axis as the twin axis. The twin boundaries appear to be fairly straight and perpendicular to the fivefold twin axis. The icosahedral twin can be expressed as a rotation of $63.4^{circ}$ or $116.62^{circ}$ around two fold zone axis.