  We study the evolution of magnetic fields in turbulent hot plasma of the
early Universe accounting for the chiral magnetic effect. The
magnetohydrodynamic turbulence is modeled by replacing the matter velocity in
the advection term in the Faraday equation with the Lorentz force. The system
of the kinetic equations for the spectra of the densities of the magnetic
helicity and the magnetic energy, as well as for the chiral imbalance, is
derived. The amplification of the magnetic field is shown to result from the
presence of the chiral magnetic effect solely. The system of the kinetic
equations is solved numerically in primordial plasma after the electroweak
phase transition. The influence of the matter turbulence on the magnetic field
evolution is examined for different seed magnetic fields.
