The method of one-center expansion of molecular wave function is applied to the calculation of electronic energies of lower excited levels, 3Σg+, 3, 1Σu+ and 3, 1Πu of H2. As for the ground 1Σg+ level the present author has already reported some calculations where he stated to have obtained the best value, 3.8 e.V., as the electronic dissociation energy. Unfortunately it was later found that there were mistakes in numerical calculations. An alternative `best' value, 3.28 e.V., will be reported in the second section of the present paper. As a whole, the results of the present calculations may be said moderately satisfiable.