The X-ray diffraction studies on a newly synthesized Na26Au25Ga29 single crystal revealed the formation of a single phase 2/1-2/1-2/1 Bergman-type approximant and the presence of Au/Ga mixed occupancies in its unit cell containing 680 atoms. The structure model of the 2/1-2/1-2/1 approximant with composition Na27Au27Ga31 was constructed by eliminating the chemical disorder with a minimum sacrifice of composition displacement. The full potential linearized augmented plane wave electronic structure calculations with subsequent full potential linearized augmented plane wave-Fourier analysis were performed for the 2/1-2/1-2/1 approximant Na27Au27Ga31 with space group P a¯3. The square of the Fermi diameter (2kF)2, electrons per atom ratio e/a and the critical reciprocal lattice vector |G|2 are determined. A shallow pseudogap at the Fermi level was interpreted as originating from interference of electrons having (2kF)2 = 109.2 ± 1.0 with sets of lattice planes with |G|2's centered at 108. The effective e/a value for the compound is found to be 1.76 in good agreement with 1.73 derived from a composition average of (e/a)Na = 1.0, (e/a)Au = 1.0 and (e/a)Ga = 3.0.