To clarify some discrepancies in the literature about the formation of icosahedral quasi-crystal (IQC) in Al–Cu–Fe alloys, microstructures, and constituent phases of Al62.5Cu25Fe12.5 and Al65Cu20Fe15 alloys were studied. Each dendritic arm of the primarily solidified λ–Al13Fe4 phase is a single crystal that possesses no definite orientation relationship with the IQC, formed by peritectic reaction (L + λ + β → IQC) or a solid-state reaction (Cu-rich phases + λ + β →?IQC). This fact disproves an assumption that λ-phase is an approximant of the IQC. Two types of cubic phase, β-phase with CsCl structure containing more Fe and τ3 phase, which is a superstructure and contains less Fe, were observed depending on the composition and thermal history of the samples.