The cross-section of associated J/ψ-ψ(2S) production in proton-proton collisions at a centre-of-mass energy of (Formula presented.) TeV is measured using a data sample corresponding to an integrated luminosity of 4.2 fb−1, collected by the LHCb experiment. The measurement is performed for both J/ψ and ψ(2S) mesons having transverse momentum pT< 14 GeV/c and rapidity 2.0 < y < 4.5, assuming negligible polarisation of the J/ψ and ψ(2S) mesons. The production cross-section is measured to be 4.5 ± 0.7 ± 0.3 nb, where the first uncertainty is statistical and the second systematic. The differential cross-sections are measured as functions of several kinematic variables of the J/ψ-ψ(2S) candidates. The results are combined with a measurement of J/ψ-J/ψ production, giving a cross-section ratio between J/ψ-ψ(2S) and J/ψ-J/ψ production of 0.274 ± 0.044 ± 0.008, where the first uncertainty is statistical and the second systematic.