  We calculated the complete next-to-leading order(NLO) QCD corrections to the
$t\bar t b \bar b$ production process at a $\gamma \gamma$ collider in the
standard model(SM). The calculation of the one-loop QCD correction includes the
evaluations of the hexagon and pentagon amplitudes. We studied the NLO QCD
corrected total cross section, the distributions of transverse momenta of final
top- and bottom-quark states, and the dependence of the cross section on
renormalization scale $\mu$. It shows that NLO QCD correction generally
increases the LO cross section in our chosen parameter space, and the K-factor
varies from 1.70 to 1.14 when colliding energy goes up from $400 GeV$ to $2
TeV$. We find that the correction distinctly changes the distributions of
transverse momenta of the final top- and bottom-quark states, and the NLO QCD
correction obviously improves the independence of the cross section for process
$\gamma\gamma \to t\bar t b\bar b$ on the renormalization scale.
