The ATLAS detector at the Large Hadron Collider is used to search for the lepton flavor violating process Z→eμ in pp collisions using 20.3  fb-1 of data collected at s=8  TeV. An enhancement in the eμ invariant mass spectrum is searched for at the Z-boson mass. The number of Z bosons produced in the data sample is estimated using events of similar topology, Z→ee and μμ, significantly reducing the systematic uncertainty in the measurement. There is no evidence of an enhancement at the Z-boson mass, resulting in an upper limit on the branching fraction, B(Z→eμ)<7.5×10-7 at the 95% confidence level.