The structure of the quasicrystalline approximant Al₁₃Co₄(100) has been determined by surface X-ray diffraction (SXRD) and complementary density functional theory (DFT) calculations. Thanks to the use of a 2D pixel detector, which speeds up enormously the data acquisition, an exceptionally large set of experimental data, consisting of 124 crystal truncation rods, have been collected and used to refine this complex structure of large unit cell and low symmetry. Various models were considered for the SXRD analysis. The best fit is consistent with a surface termination at the puckered-type of planes but with a depletion of the protruding Co atoms. The surface energy of the determined surface model was calculated by DFT and takes a rather low value of 1.09 J/m². Results for atomic relaxation of surface planes found by SXRD or DFT were in excellent agreement. This work opens new perspectives for the comprehension of related quasicrystalline surfaces.