One of the most challenging tasks for future high-luminosity electron-positron colliders is to extract Higgs triple coupling. It was proposed that this can be carried out via the precisely measuring the cross section of ZH associated production up to $0.4\%$. In this paper, we example the possible heavy pollution from Higgs-top anomalous coupling. Our numerical results show that the pollution is small for $\sqrt{s}_{e^+e^-}= 240 GeV$. However for the higher energy collider, pollution is sizable, which should be taken into account. We further explored the possibility to measure CP-violated Higgs top coupling, via the forward-backward asymmetry $A_{FB}$ for the process $e^+e^- \rightarrow ZH$. The asymmetry can reach $0.7\%$ which is comparable to the precision of cross section measurement.

10 pages, 6 figures, discussions and references added, published in Phys. Rev. D