We have investigated the possible applications potential of a newly developed bcc-nanocrystalline Fe₈₆Zr₇B₆Cu₁ alloy by determining the core loss, permeability μ_e, and magnetization B₈₀₀ (at a field 800 kA/m). The above parameters have been studied as a function of annealing temperature T_a of the as-quenched amorphous alloy, maximum induction B_m, and frequency (up to 100 kHz). On transformation to the bcc-nanocrystalline state at 873 K with a 10 nm grain size, maximum values of μ_e=41000 and B₈₀₀=1.52 T are obtained. The determined core loss is found to achieve a minimum value of 66 mW/kg at 1 T, 50 Hz. This value is considerably smaller (45 and 95% respectively) than those reported for the amorphous Fe₇₈Si₉B₁₃ and bcc Fe–3.5%Si alloys now in use as transformer core materials. The observed B_m and frequency dependences of the loss values for our new Fe–Zr–B–Cu alloy are consistently found to be superior as well. Thus, the bcc-nanocrystalline Fe–Zr–B–Cu alloy is quite promising for practical use as a core material in various transformers with the advantage of high B₈₀₀, high μ_e and low core loss.