  The cross section for process $e^+e^-\to\mu^+\mu^-\gamma$ in the framework of
noncommutative quantum electrodynamics(NC QED) is studied. It is shown that the
NC correction of scattering sections is not monotonous enhancement with total
energy of colliding electrons, but there is an optimal collision energy to get
the greatest NC correction. Moreover, there is a linear relation between NC QED
scale energy and the optimal collision energy. The experimental methods to
improve the precision of determining NC effects are discussed, because this
process is an ${\cal O}(\alpha^3) $ NC QED process, high precision tests are
necessary.
