  A high luminosity Circular Electron Positron Collider (CEPC) as a Higgs
Factory will be helpful to the precision measurement of the Higgs mass. The
signal-background interference effect is carefully studied for the Higgs
diphoton decay mode in the associated Z boson production at the future $e^+e^-$
colliders at energy $246 {\rm GeV}$. The mass shifts go up from about $20 {\rm
MeV}$ to $50 {\rm MeV}$ for the experimental mass resolution ranging from $0.8
{\rm GeV}$ to $2 {\rm GeV}$.
