Abstract : A new perspective for the anharmonic oscillator problem based on the SU(2) group method (SGM) is provided. One finds that the SGM is a possible unified approach to treat both the harmonic oscillator and the anharmonic oscillator, although for the latter only part of the energy spectrum can be obtained. Coordinate translation x → x + λ for the anharmonic potential is also discussed, as one expects that the energy spectrum of an anharmonic oscillator is not affected by the translation.