  In this paper,we show that spherical bounded energy solution of the
defocusing 3D energy critical Schr\"odinger equation with harmonic potential,
$(i\partial_t + \frac {\Delta}2+\frac {|x|^2}2)u=|u|^4u$, exits globally and
scatters to free solution in the space $\Sigma=H^1\bigcap\mathcal F H^1$. We
preclude the concentration of energy in finite time by combining the energy
decay estimates.
