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+1.8−1.3)×10−8, where statistical and systematic uncertainties are included, which is consistent with the standard model prediction.