A measurement of the angular distribution of leptons from the analysis of W-boson decay data is presented. Although the properties of the leptonic angular distribution from W decays have been studied extensively in the past decades, the amount of data collected at the Tevatron is sufficient to observe Quantum Chromo Dynamics (QCD) corrections. When QCD is included, the lepton polar-angle distribution is best described by two parameters, α1 and α2, functions of pWT: (dσ/d cosθ*) α (1 ± α1 cosθ* + α2 cos2θ*) where θ* is measured in the W rest-frame with respect to the proton beam. Both the W asymmetry measurement and the W mass precision measurement at CDF rely on the accurate understanding and simulation of the leptonic angular distribution. The data analysed in this thesis, which include both the electron and the muon channels, were collected with the CDF detector at the Tevatron proton-antiproton collider during Run Ib (1994-1996). The coefficient α2 of the polar-angle distribution is measured as a function of the W-boson transverse-momentum up to 100 GeV. The measurement strategy consists of fitting the transverse-mass distribution to a set of templates from a Monte Carlo event and detector simulation. A log-likelihood method is used to determine α2. The measured values of α2 confirm the Standard Model expectation for the W-polarisation at high transverse-momentum. A study for a measurement of α1 is also presented. However, there is insufficient sensitivity for the measurement of α1 with the CDF Run I detector.