With the deeper study of Higgs particle, Higgs precision measurements can be served to probe new physics indirectly. In many new physics models, vectorlike quarks T L , T R occur naturally. It is important to probe their couplings with standard model particles. In this work, we consider the singlet T L , T R extended models and show how to constrain the Tth couplings through the h → γZ decay at high-luminosity LHC. First, we derive the perturbative unitarity bounds on jy tT L;R j with other couplings set to be zeros simply. To optimize the situation, we take m T ¼ 400 GeV and s L ¼ 0.2 considering the experimental constraints. Under this benchmark point, we find that the future bounds from h → γZ decay can limit the real parts of y tT L;R in the positive direction to be O(1) because of the double enhancement. For the real parts of y tT L;R in the negative direction, it is always surpassed by the perturbative unitarity. Moreover, we find that the top quark electric dipole moment can give stronger bounds (especially the imaginary parts of y tT L;R) than the perturbative unitarity and h → γZ decay in the off-axis regions for some scenarios.