A rigorous solution of Schrdinger equation of an spheresymmetry harmonic oscillator is studied by the power series method.We found that wave function ψ(r,θ,φ)|r～0 can be infinite, rψ(r,θ,φ)|r～0 must be finite; this is in accord with Born's statistical explanation. The groundstate energy of the spheresymmetry harmonic oscillator is ω/2. The space dent will appear in the ground state of the spheresymmetry harmonic oscillator.