A search for the D-0 -> pi(+)pi(-)mu(+)mu(-) decay, where the muon pair does not originate from a resonance, is performed using proton-proton collision data corresponding to an integrated luminosity of 1.0 fb(-1) recorded by the LHCb experiment at a centre-of-mass energy of 7 TeV. No signal is observed and an upper limit on the relative branching fraction with respect to the resonant decay mode D-0 -> pi(+)pi(-)phi(-> mu(+)mu(-)), under the assumption of a phase-space model, is found to be B(D-0 -> pi(+)pi(-)mu(+)mu(-))/B(D-0 -> pi(+)pi(-)phi(-> mu(+)mu(-))) < 0.96 at 90% confidence level. The upper limit on the absolute branching fraction is evaluated to be B(D-0 -> pi(+)pi(-)mu(+)mu(-)) < 5.5 x 10(-7) at 90% confidence level. This is the most stringent to date. (C) 2013 The Authors. Published by Elsevier B.V. All rights reserved.