  We discuss the generation of large-scale magnetic fields due to the breaking
of the conformal invariance in the electromagnetic field through the $CPT$-even
dimension-six Chern-Simons-like effective interaction with a fermion current in
inflationary cosmology. It is shown that the magnetic fields on 1Mpc scale with
the field strength of $\sim 10^{-9}$G at the present time can be generated even
for the scale of the effective interaction being the Planck scale.
