Stellar metallicity is known to play a significant role in age determinations for different Galactic stellar populations when main sequence evolutionary tracks are employed. However, such a study was lacking for the case in which the age of the Galactic disk is estimated using the position of the cut-off of the white dwarf luminosity function. We try to fill this gap by exploring the possible dependence of the overall shape and cut-off position of the white dwarf luminosity function on the adopted age-metallicity relationship by using a Monte Carlo population simulator.