A search for the rare leptonic decay B+→μ+μ−μ+νμ is performed using proton-proton collision data corresponding to an integrated luminosity of 4.7fb−1 collected by the LHCb experiment. The search is carried out in the region where the lowest of the two μ+μ− mass combinations is below 980MeV/c2 . The data are consistent with the background-only hypothesis and an upper limit of 1.6×10−8 at 95% confidence level is set on the branching fraction in the stated kinematic region.