Display omitted Using proton-proton collision data at centre-of-mass energies of s=7,8 and 13TeV recorded by the LHCb experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 9fb-1, the invariant mass spectrum of J/ψ pairs is studied. A narrow structure around 6.9GeV/c2 matching the lineshape of a resonance and a broad structure just above twice the J/ψ mass are observed. The deviation of the data from nonresonant J/ψ-pair production is above five standard deviations in the mass region between 6.2 and 7.4GeV/c2, covering predicted masses of states composed of four charm quarks. The mass and natural width of the narrow X(6900) structure are measured assuming a Breit-Wigner lineshape.