The three different helicity states of W bosons produced in the reaction e+e-→lvqq at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies √s=183–209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218±0.027±0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation.