A study is presented of central exclusive production of Υ(nS) states, where the Υ(nS) resonances decay to the μ + μ − final state, using pp collision data recorded by the LHCb experiment. The cross-section is measured in the rapidity range 2 < y(Υ) < 4.5 where the muons are reconstructed in the pseudorapidity range 2 < η(μ ±) < 4.5. The data sample corresponds to an integrated luminosity of 2.9 fb−1 and was collected at centre-of-mass energies of 7 TeV and 8 TeV. The measured Υ(1S) and Υ(2S) production cross-sections are $$ \sigma \left( pp\to pY(1S)p\right)=9.0\pm 2.1\pm 1.7\kern0.5em \mathrm{p}\mathrm{b}\kern0.5em \mathrm{and}\kern0.5em \sigma \left( pp\to pY(2S)p\right)=1.3\pm 0.8\pm 0.3\kern0.5em \mathrm{p}\mathrm{b}, $$ where the first uncertainties are statistical and the second are systematic. The Υ(1S) crosssection is also measured as a function of rapidity and is found to be in good agreement with Standard Model predictions. An upper limit is set at 3.4 pb at the 95% confidence level for the exclusive Υ(3S) production cross-section, including possible contamination from χ b (3P ) → Υ(3S)γ decays.