We employed atomistic simulations to study the formation of a double-kink (DK) on a screw dislocation in bcc-Fe and to investigate how the presence of Cr affects it, using one of the most recent and reliable interatomic potentials for Fe and Fe–Cr systems. The formation energy of a DK of different lengths and structures, as well as the formation energies of each single kink and the interaction energies between them, have been obtained by performing large scale atomistic simulations and compared with the results obtained from elasticity theory. We show that the presence of Cr atoms, particularly Cr–Cr pairs, affects, sometimes significantly, the formation energy of DKs. The results suggest a strong dependence of the effect of solute Cr atoms on dislocation motion in Fe–Cr alloys, depending on the actual Cr distribution, which depends strongly on concentration and temperature. A framework to understand solute softening and hardening experimentally observed in Fe–Cr alloys is accordingly discussed.