A new ring-shaped harmonic oscillator potential is proposed. Under the condition of equal scalar and vector potentials, the exact bound state solutions and the energy spectrum of the Klein-Gordon equation with this oscillator potential are obtained by the factorization method. It is shown that both the angular and radial wave functions are expressed in terms of the elementary functions respectively. The energy equation is analyzee with the Descarte′s rule of signs and it is shown that for given values of M and n only discrete, positive energies are allowed.

ring-shaped harmonic oscillator potential; Klein-Gordon equation; factorization method; bound state