© 2018 CERN, for the LHCb Collaboration. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 . A search for the rare decay Σ+→pμ+μ- is performed using pp collision data recorded by the LHCb experiment at center-of-mass energies s=7 and 8 TeV, corresponding to an integrated luminosity of 3 fb-1. An excess of events is observed with respect to the background expectation, with a signal significance of 4.1 standard deviations. No significant structure is observed in the dimuon invariant mass distribution, in contrast with a previous result from the HyperCP experiment. The measured Σ+→pμ+μ- branching fraction is (2.2-1.3+1.8)×10-8, where statistical and systematic uncertainties are included, which is consistent with the standard model prediction.