Aims. We analyzed the effect of the sedimentation of²²Ne on the local white dwarf luminosity function by studying scenarios under different Galactic metallicity models.Methods. We use an advanced population synthesis code based on Monte Carlo techniques to derive the synthetic luminosity function. The code incorporates the most recent and reliable cooling sequences and an accurate modeling of the observational biases under different scenarios. We first analyzed the case for a model with constant solar metallicity and compared the models with and without²²Ne sedimentation with the observed luminosity function for a pure thin-disk population. Then we analyzed the possible effects of a thick-disk contribution. We also studied model scenarios with different metallicities, including²²Ne sedimentation. The analysis was quantified from a statisticalχ²-test value for the complete and also for the most significant regions of the white dwarf luminosity function. Finally, a best-fit model along with a disk age estimate was derived.Results. Models with constant solar metallicity cannot simultaneously reproduce the peak and cutoff of the white dwarf luminosity function. The additional release of energy due to²²Ne sedimentation piles up more objects in brighter bins of the faint end of the luminosity function. The contribution of a single-burst thick-disk population increases the number of stars in the magnitude interval centered aroundM_bol = 15.75. The metallicity model that follows a Twarog profile is disposable. Our best-fit model was obtained when a dispersion in metallicities of about solar metallicity was considered along with a²²Ne sedimentation model, a thick-disk contribution, and an age of the thin disk of 8.8 ± 0.2 Gyr.Conclusions. Our population synthesis model is able to reproduce the local white dwarf luminosity function with a high degree of precision when a dispersion in metallicities around a model with solar values is adopted. Although the effects of²²Ne sedimentation are only marginal and the contribution of a thick-disk population is minor, both of them help in better fitting the peak and the cutoff regions of the white dwarf luminosity function.