  A precise calculation of the top quark pair production associated with a hard
photon is essential for testing the electroweak property of the top quark in
the Standard Model (SM). We investigate the one-loop QCD corrections to the
process $e^{+}e^{-} \to t\bar{t}\gamma$ at the International Linear Collider
(ILC), and find that the $K$-factor can be as large as 1.238 (1.105, 1.060) for
a center-of-mass energy $\sqrt{s}=500 (800, 1500)$ GeV. The transverse momentum
distributions of the top quark and photon are respectively shown at leading
order (LO) and next-to-leading order(NLO). Due to the asymmetric rapidity
distribution of the top (anti-top) quark, we also study the top quark
forward-backward asymmetry ($A^{t}_{FB}$) in $t\bar{t}\gamma$ production at
NLO, which is found to be 45.82 (55.25, 55.89)% for $\sqrt{s}=500 (800, 1500)$
GeV.
