We report an angle-resolved photoemission study of BaFe2As 2, a parent compound of iron-based superconductors. Low-energy tunable excitation photons have allowed the first observation of three-dimensional saddle-point dispersion at the Z point, as well as the Γ point. This resolves a discrepancy in Fermi-surface studies. We found that these van Hove singularities are not only involved in three-dimensional Fermi-surface reconstruction with antiferromagnetic ordering but also renormalized and predominant at low energies. Hence, the Fermi-surface instability due to these singularities would also underlie the associated superconductors. © 2013 Elsevier Ltd.