We investigate an inflationary model of the universe based on the assumption that space-time is noncommutative in the very early universe. We analyze the effects of space-time noncommutativity on the quantum fluctuations of an inflaton field and investigate their contributions to the cosmic microwave background (CMB). We show that the angular power spectrum l(l + 1)C(l) generically has a sharp damping for lower l if we assume that the last scattering surface is traced back to fuzzy spheres at the times when large-scale modes cross the Hubble horizon. (C) 2004 Elsevier B.V. All rights reserved.