The two-electron self-energy contribution to the ground-state energy of helium-like ions is calculated both for a point nucleus and an extended nucleus in a wide interval of Z. All the two-electron contributions are compiled to obtain most accurate values for the two-electron part of the ground-state energy of helium-like ions in the range Z = 20-100. The theoretical value of the ground-state energy of ²³⁸U⁹⁰⁺, based on currently available theory, is evaluated to be - 261382.9(8) eV, without higher-order one-electron QED corrections.