  We study the effects of T-odd interactions of top-quark via the pair
production of top-quark in the semileptonic detection modes at the Large Hadron
Collider by means of the T-odd observables constructed through the momenta of
the observed decay products of the top (and anti-top)-quark for a wide range of
CP-violating scale $\Lambda$. Estimates on the sensitivities of the coupling
strength of such interactions for 13 TeV LHC energy with $\int \mathcal L dt$ =
36.1 fb$^{-1}$, 140 fb$^{-1}$ and for HL-LHC with 14 TeV energy with integrated
luminosities of 0.3 ab$^{-1}$, 1 ab$^{-1}$, 2 ab$^{-1}$ and 3 ab$^{-1}$ are
also presented for $\Lambda$ ranging between $M_W$ and 2 TeV.
