  The $g$-extra connectivity is an important parameter to measure the ability
of tolerance and reliability of interconnection networks. Given a connected
graph $G=(V,E)$ and a non-negative integer $g$, a subset $S\subseteq V$ is
called a $g$-extra cut of $G$ if $G-S$ is disconnected and every component of
$G-S$ has at least $g+1$ vertices. The cardinality of the minimum $g$-extra cut
is defined as the $g$-extra connectivity of $G$, denoted by $\kappa_g(G)$. In a
search for triangle-free graphs with arbitrarily large chromatic numbers,
Mycielski developed a graph transformation that transforms a graph $G$ into a
new graph $\mu(G)$, which is called the Mycielskian of $G$. This paper
investigates the relationship of the g-extra connectivity of the Mycielskian
$\mu(G)$ and the graph $G$, moreover, show that
$\kappa_{2g+1}(\mu(G))=2\kappa_{g}(G)+1$ for $g\geq 1$ and $\kappa_{g}(G)\leq
min\{g+1, \lfloor\frac{n}{2}\rfloor\}$.
