We have obtained La1.95Bi0.05CuO4+δ with various values of δ by the KMnO4 oxidation method. The largest value of δ≈0.136 is about twice as large as that obtained by annealing under high pressures of oxygen, δ≈0.056. A structural phase transition from the orthorhombic to the tetragonal phase with the increase of δ is observed at δ=0.035-0.04. For δ≳0.08, another orthorhombic phase with large orthorhombic distortion appears and forms a mixture with the tetragonal phase. Superconductivity appears in the range of δ≳0.03. In the mixture range of δ≳0.08, however, the orthorhombic phase may exhibit no superconductivity due to the overdoping of hole carriers into the CuO2 plane. The maximum Tc increases up to ∼35 K, which is about 10 K higher than that obtained by annealing under high pressures of oxygen, owing to the larger hole concentration in the CuO2 plane.