  We suggest a new mean field dynamo model in anomalous MagnetoHydroDynamics
(AMHD) accounting for the mean spin (polarization) of the magnetized chiral
(ultrarelativistic) plasma of a neutron star (NS). For simplicity we consider a
non-superfluid NS with its rigid rotation neglecting also any matter turbulence
(convection) within a star. On this way, we recover the Chiral Magnetic Effect
(CME) as a possible source for the amplification of a seed, sufficiently strong
magnetic field, $B\sim 10^{13}\,\text{G}$, up to values $B\gtrsim
10^{18}\,\text{G}$ in old NS's, having ages $t\gtrsim 10^6\,\text{yr}$. The
important issue in AMHD model suggested is the continuous evolution of the
chiral imbalance providing the CME for these ages, $\partial_t\mu_5 (t)\neq 0$,
in spite of the fast spin-flip in Coulomb collisions in the dense NS plasma
that leads to vanishing $\mu_5\to 0$ at an earlier epoch in the corresponding
protoneutron star. In contrast to the conventional mean-field dynamos, the
dynamo drivers in the model are produced due to magnetic field generated at the
previous stages of stellar evolution. It makes our model basically nonlinear.
