Reed [B. Reed, ω,Δ and χ, Journal of Graph Theory, 27 (1998) 177-212] conjectured that for any graph G, χ(G)≤Δ(G) +ω(G)+12⌉, where χ(G), ω(G), and Δ(G) respectively denote the chromatic number, the clique number and the maximum degree of G. In this paper, we verify this conjecture for some special classes of graphs which are defined by families of forbidden induced subgraphs. © 2011 Elsevier B.V. All rights reserved.