  In 1998, Reed conjectured that for any graph $G$, $\chi(G) \leq \lceil
\frac{\omega(G) + \Delta(G)+1}{2}\rceil$, where $\chi(G)$, $\omega(G)$, and
$\Delta(G)$ respectively denote the chromatic number, the clique number and the
maximum degree of $G$. In this paper, we study this conjecture for some
expansions of graphs, that is graphs obtained with the well known operation
composition of graphs.
  We prove that Reed's Conjecture holds for expansions of bipartite graphs, for
expansions of odd holes where the minimum chromatic number of the components is
even, when some component of the expansion has chromatic number 1 or when a
component induces a bipartite graph. Moreover, Reed's Conjecture holds if all
components have the same chromatic number, if the components have chromatic
number at most 4 and when the odd hole has length 5. Finally, when $G$ is an
odd hole expansion, we prove
$\chi(G)\leq\lceil\frac{\omega(G)+\Delta(G)+1}{2}\rceil+1$.
