  We study the existence of multi-bubble solutions for the following
skew-symmetric Chern--Simons system \begin{equation}\label{e051} \left\{
\begin{split} &\Delta
u_1+\frac{1}{\varepsilon^2}e^{u_2}(1-e^{u_1})=4\pi\sum_{i=1}^{2k}\delta_{p_{1,i}}\\
&\Delta
u_2+\frac{1}{\varepsilon^2}e^{u_1}(1-e^{u_2})=4\pi\sum_{i=1}^{2k}\delta_{p_{2,i}}
\end{split} \text{ in }\quad \Omega\right., \end{equation} where $k\geq 1$ and
$\Omega$ is a flat tours in $\mathbb{R}^2$. It continues the joint work with
Zhang\cite{HZ-2015}, where we obtained the necessary conditions for the
existence of bubbling solutions of Liouville type. Under nearly necessary
conditions(see Theorem \ref{main-thm}), we show that there exist a sequence of
solutions $(u_{1,\varepsilon}, u_{2,\varepsilon})$ to \eqref{e051} such that
$u_{1,\varepsilon}$ and $u_{2,\varepsilon}$ blow up simultaneously at $k$
points in $\Omega$ as $\varepsilon\to 0$.
