Abstract Low-temperature resistivities, in zero-field and 8 T field, and magnetoresistance have been measured down to 1.4–300 K for stable icosahedral quasicrystals Al 65Cu 20+ x Ru 15− x ( x = 1.5, 1.0, 0.5, 0.0 and −0.5). The analysis of the magnetoresistance data shows an overwhelming presence of anti weak-localization effect ( τ so ∼ 10 −12 s). But the sample with x = −0.5 shows anomalous magnetoresistance and the anti weak-localization effect breaks down ( τ so to be 10 −15 s). The in-field σ– T between 5 K and 20 K, for x = 1.0, 0.5, 0.0 and −0.5 samples, and between 1.4 K and 40 K for x = 1.5 sample, follow a power-law behavior with an exponent of 0.5 and above ∼30 K the exponent ranges from 1.17 to 1.58. The observed power-laws basically characterize the presence of critical regime of the metal–insulator (MI) transition, dominated by electron–electron and electron–phonon inelastic scattering events respectively. In samples with x = 1.0, 0.5, 0.0 and −0.5 the in field σ– T has been found to follow ln σ-vs- T 1/4 below 5 K, which indicates the presence of variable range hopping. The observed transport features indicate the occurrence of proximity of metal–insulator transition in these Al–Cu–Ru quasicrystal samples.