The elastic scattering and breakup of the halo nucleus 11 Be on protons at an incident energy of 26.9A MeV have been measured. The 11 Be +p elastic scattering cross sections at various energies, including the present one, are systematically analyzed with the Chapel Hill 89 (CH89) and Koning-Delaroche (KD) global optical model potentials (OMPs), and the corresponding normalization factors are obtained. An extended version of the continuum-discretized coupled-channels (XCDCC) formalism, including dynamic core excitation effects, is applied to analyze the elastic scattering and breakup data. It is found that the core excitation plays a moderate role in the elastic scattering and breakup reaction of the halo nucleus 11 Be, being consistent with previous results at higher energies.