The ATLAS detector at the Large Hadron Collider is used to search for the lepton flavor violating process Z -> e mu in pp collisions using 20.3 fb(-1) of data collected at root s = 8 TeV. An enhancement in the e mu 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 mu mu, 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 -> e mu) < 7.5 x 10(-7) at the 95\% confidence level.