We utilise the LHC Run-1 and -2 Higgs data to constrain the CP-violating top-Higgs couplings.In order to satisfy the current full Higgs data sets at 2σ level, the CP-odd component C With the new bound, we explore the impact on the CP-violating top-Higgs couplings in the Higgs production processes pp → tth, thj, hh at 13 TeV LHC, and e + e − → hZ, hγ at future 240 GeV Higgs factories. We find that the cross sections of pp → tth, pp → thj, pp → hh, e + e − → hZ and e + e − → hγ can be enhanced up to 1.41, 1.18, 2.20, 1.001 and 1.09 times as large as the SM predictions, respectively. The future precision measurement of the process e + e − → hγ with an accuracy of 5% will be able to constrain |C p t | < 0.19 at most at a 240 GeV e + e − Higgs factory.