Low-cycle fatigue behavior of a wrought Al-0.8wt%Mg-0.7wt%Si alloy with and without 0.27wt%Sc has been investigated at room temperature under constant plastic-strain amplitudes. After peak-aging treatments, both the alloys had fine lath-shaped β' precipitates. In the Sc-containing alloy, spherical Al3Sc precipitates of about 11 nm in diameter were co-existed. The alloy with Sc exhibited cyclic hardening to saturation, while the alloy without Sc showed clear cyclic softening after initial hardening. Transmission electron microscopy observation revealed that slip band structures were developed in the Sc-free alloy. Within the slip bands, shearing of the β' precipitates by moving dislocations was often observed. The cyclic softening in the alloy without Sc can then be explained by a loss of precipitation strengthening effect through the precipitation destruction within strongly-strained slip bands. In the Sc-bearing alloy, owing to the existence of non-shearable Al3Sc precipitates, dislocations were uniformly distributed, resulting in the absence of the cyclic softening.