A coupling of a dark photon A from a U(1) A with the standard model (SM) particles can be generated through kinetic mixing represented by a parameter . A non-zero also induces a mixing between A and Z if dark photon mass m A is not zero. This mixing can be large when m A is close to m Z even if the parameter is small. Many efforts have been made to constrain the parameter for a low dark photon mass m A compared with the Z boson mass m Z . We study the search for dark photon in e + e − → γA → γµ + µ − for a dark photon mass m A as large as kinematically allowed at future e + e − colliders. For large m A , care should be taken to properly treat possible large mixing between A and Z. We obtain sensitivities to the parameter for a wide range of dark photon mass at planed e + e − colliders, such as Circular Electron Positron Collider (CEPC), International Linear Collider (ILC) and Future Circular Collider (FCC-ee). For the dark photon mass 20 GeV m A 330 GeV, the 2σ exclusion limits on the mixing parameter are 10 −3 -10 −2 . The CEPC with √ s = 240 GeV and FCC-ee with √ s = 160 GeV are more sensitive than the constraint from current LHCb measurement once the dark photon mass m A 50 GeV. For m A 220 GeV, the sensitivity at the FCC-ee with √ s = 350 GeV and 1.5 ab −1 is better than that at the 13 TeV LHC with 300 fb −1 , while the sensitivity at the CEPC with √ s = 240 GeV and 5 ab −1 can be even better than that at 13 TeV LHC with 3 ab −1 for m A 180 GeV. We also comment on sensitivities of e + e − → γA with dark photon decay into several other channels at future e + e − colliders.