Precise predictions for an $e^+e^-rightarrow tbar{t}$ cross section are presented at an energy region from 400 GeV to 800 GeV. Cross sections are estimated including the beam-polarization effects with full $mathcal{O}(alpha)$, and also with effects of the initial-state photon emission. A radiator technique is used for the initial-state photon emission up to two-loop order. A weak correction is defined as the full electroweak corrections without the initial-state photonic corrections. As a result, it is obtained that the total cross section of a top quark pair-production receives the weak corrections of $+4%$ over the trivial initial state corrections at a centre of mass energy of 500 GeV. Among the initial state contributions, a contribution from two-loop diagrams gives less than $0.11%$ correction over the one-loop ones at the center of mass energies of from $400$ GeV to $800$ GeV. In addition, an effect of a running coupling constant is also discussed.
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