  A proper coloring of the vertices of a graph is called a \emph{star coloring}
if the union of every two color classes induces a star forest. The star
chromatic number $\chi_s(G)$ is the smallest number of colors required to
obtain a star coloring of $G$. In this paper, we study the relationship between
the star chromatic number $\chi_s(G)$ and the maximum average degree
$\mbox{Mad}(G)$ of a graph $G$. We prove that: (1) If $G$ is a graph with
$\mbox{Mad}(G) < \frac{26}{11}$, then $\chi_s(G)\leq 4$. (2) If $G$ is a graph
with $\mbox{Mad}(G) < \frac{18}{7}$ and girth at least 6, then $\chi_s(G)\leq
5$. (3) If $G$ is a graph with $\mbox{Mad}(G) < \frac{8}{3}$ and girth at least
6, then $\chi_s(G)\leq 6$. These results are obtained by proving that such
graphs admit a particular decomposition into a forest and some independent
sets.
