Abstract: The inclusion form of L_p-centroid bodies is introduced, and its reverse f
orm discussed. An inclusion of the form (p-1)c_nΓ_∞K(p-1)Γ_pK(q-1)Γ_qK(q-1)c_pΓK is established, where1≤n≤p≤q≤∞and c_p，c_n are universal constants depending only on p,n respectively. Furthermore, boundness of the volume of the central section is estimated with the support function of L_p-centroid bodies.

Key words: L_p-centroid bodies, reverse inclusion, slicing problem, convex bodies