In this paper, we introduce the notion of bounded Betti numbers, and show that the bounded Betti numbers of a closed Riemannian n-manifold (M, g) with Ric (M) ≥-(n - 1) and Diam (M) ≤ D are bounded by a number depending on D and n. We also show that there are only finitely many isometric isomorphism types of bounded cohomology Diam (M) ≤ D.