Abstract: Three kinds of deformed harmonic oscillator potentials are given： left and right part with different parameters,left square potential and right harmonic oscillator potential,harmonic oscillator potential plus delta potential.The eigen-state of these potentials can be expressed in terms of the Hermite function.The energy spectrum equations are derived from the matching condition of wave function and its first derivative at origin.

Key words: deformed harmonic oscillator potential, Hermite function, energy spectrum equation