  The unitary S-matrix for the space-time non-commutative QED is constructed
using the $\star$-time ordering which is needed in the presence of derivative
interactions. Based on this S-matrix, perturbation theory is formulated and
Feynman rule is presented. The gauge invariance is explicitly checked to the
lowest order, using the Compton scattering process. The gauge fixing condition
dependency of the classical solution of the vacuum is also discussed.
