  We study the pairwise quantum discord (QD) for a symmetric multi-qubit system
in different types of noisy channels, such as phase-flip, amplitude damping,
phase-damping, and depolarizing channels. Using the QD and geometric measure of
quantum discord (GMQD) to quantify quantum correlations, some analytical or
numerical results are presented. The results show that, the dynamics of the
pairwise QD is related to the number of spin particles $N$ as well as initial
parameter $\theta$ of the one-axis twisting collective state. With the number
of spin particles $N$ increasing, the amount of the pairwise QD increases.
However, when the amount of the pairwise QD arrives at a stable maximal value,
the pairwise QD is independence of the number of spin particles $N$ increasing.
The behavior of the pairwise QD is symmetrical during a period $0\leq \theta
\leq 2\pi$. Moreover, we compare the pairwise QD dynamics with the GMQD for a
symmetric multi-qubit system in different types of noisy channels.
