Abstract: A study of the decay D-0 -> K-pi(+)mu(+)mu(-) is performed using data collected by the LHCb detector in proton-proton collisions at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2.0 fb(-1). Decay candidates with muon pairs that have an invariant mass in the range 675-875 MeV/c(2) are considered. This region is dominated by the rho(0) and omega resonances. The branching fraction in this range is measured to be B(D-0 -> K-pi(+)mu(+)mu(-)) = (4.17 +/- 0.12 (stat) +/- 0.40 (syst)) x 10(-6). This is the first observation of the decay D-0 -> K-pi(+)mu(+)mu(-). Its branching fraction is consistent with the value expected in the Standard Model.