The inclusive production of four isolated charged leptons in pp collisions is analysed for the presence of hard double-parton scattering, using 20.2 fb−1 of data recorded in the ATLAS detector at the LHC at centre-of-mass energy s=8 TeV. In the four-lepton invariant-mass range of 80<1000 GeV, an artificial neural network is used to enhance the separation between single- and double-parton scattering based on the kinematics of the four leptons in the final state. An upper limit on the fraction of events originating from double-parton scattering is determined at 95% confidence level to be fDPS=0.042 , which results in an estimated lower limit on the effective cross section at 95% confidence level of 1.0 mb.