The results of computer simulations of lower hybrid current drive (LHCD) for ITER parameters are presented. The damping of LH waves by alpha particles due to the interaction at high cyclotron resonances is obtained by solving the 2-D Fokker-Planck equation with the corresponding quasi-linear term (FPA code). This code is incorporated into a spatially 1-D LHCD code so as to obtain radial profiles of the radiofrequency (RF) power absorbed by electrons (1-D Fokker-Planck code) and alpha particles as well as the radial profile of the driven current. One-pass absorption is assumed and verified by a detailed analysis of LH rays for an ITER-like magnetic configuration. Noticeable absorption by alpha paraticles is observed only below ∼5 GHz of the generator frequency and is still acceptable down to ∼3 GHz (19% of the input power Pin, with a 16% reduction of the total driven current for Pin = 50 MW). Two competing quasi-linear effects influence the damping rates: the RF field reduces the slopes of the alpha particle distribution function but, since the absorption is accompanied by acceleration of groups of alpha particles above their initial velocity, the RF field also increases the number of resonant particles. Both the global results and the damping rates are compared with those obtained for unmagnetized alpha particles and with the linear approximation. For frequencies above ∼3 GHz, the latter approach was found to significantly overestimate the absorption by alpha particles. Some further mechanisms not included in the code but having possible effects on the interaction are also discussed.