Large top-quark flavor changing through neutral currents is expected by many extensions of the standard model. Direct and indirect searches for flavor-changing neutral currents (FCNC) in the top-quark decays to an up-type quark (up, charm) and a Higgs boson are presented. We probe the observability of the top-Higgs FCNC couplings through the process e−e+→t(→ℓνℓb)t¯(→qH), where ℓ=e, μ and q reflects up and charm quarks. It is shown that the branching ratio Br(t→qH) can be probed down to 1.12×10−3 at 95% C.L. at the center-of-mass energy of 500 GeV with an integrated luminosity of 3000 fb−1. We also update the constraint on the top-Higgs FCNC coupling using the electroweak precision observables related to Z→cc¯ decay.