We have investigated the superconducting (SC) gap on hole Fermi surfaces (FSs) of optimally substituted Ba(Fe_0.65Ru_0.35)₂As₂ by angle-resolved photoemission spectroscopy (APRES) using bulk-sensitive 7 eV laser and synchrotron radiation. It was found that, whereas the gap is isotropic in the k_x − k_y plane, the gap magnitudes of two resolved hole FSs show similar k_z dependences and decrease as k_z approaches ∼ 2π/c (i.e., around the Z point), unlike the other Fe-based superconductors reported so far, where the SC gap of only one hole FS shows a strong k_z dependence. This unique gap structure can be understood in the scenario that the d_z² orbital character is mixed into both hole FSs due to finite spin-orbit coupling (SOC) and is reproduced by calculation within the random phase approximation including the SOC.