  We study the chiral-imbalance and the Weibel instabilities in presence of the
quantum anomaly using the Berry-curvature modified kinetic equation. We argue
that in many realistic situations, e.g. relativistic heavy-ion collisions, both
the instabilities can occur simultaneously. The Weibel instability depends on
the momentum anisotropy parameter $\xi$ and the angle ($\theta_n$) between the
propagation vector and the anisotropy direction. It has maximum growth rate at
$\theta_n=0$ while $\theta_n=\pi/2$ corresponds to a damping. On the other hand
the pure chiral-imbalance instability occurs in an isotropic plasma and depends
on difference between the chiral chemical potentials of right and left-handed
particles. It is shown that when $\theta_n=0$, only for a very small values of
the anisotropic parameter $\xi\sim \xi_c$, growth rates of the both
instabilities are comparable. For the cases $\xi_c<\xi\ll1$, $\xi\approx 1$ or
$\xi \geq 1$ at $\theta_n=0$, the Weibel modes dominate over the
chiral-imbalance instability if $\mu_5/T\leq1$. However, when $\mu_5/T\geq1$,
it is possible to have dominance of the chiral-imbalance modes at certain
values of $\theta_n$ for an arbitrary $\xi$.
