Abstract. We prove that the Hausdorff operator generated by a function φ is bounded on the real Hardy space H p (R), 0 < p ≤ 1, if the Fourier transform φ of φ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on H p (R), 2/(2α + 1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of H p (R).