Abstract Whole‐genome duplication is a common mutation in eukaryotes with far‐reaching phenotypic effects. The resulting morphological, physiological and fitness consequences and how they affect the survival probability of polyploid lineages are intensively studied, but little is known about the effect of genome doubling on the evolutionary potential of populations. Historically, it has been argued polyploids should be less able to adapt because gene duplication dilutes the effects of alleles, such that polyploids are less likely to evolve new adaptive gene complexes compared with diploids. In this paper, I investigate the short‐ and long‐term consequences of genome doubling on the additive genetic variance of populations. To do so, I extended the classical models of quantitative traits under stabilizing selection to study the evolution of the additive variance of the trait under study after a shift from diploidy to tetraploidy. I found that, for realistic allele‐dosage effects, polyploidization is associated with an initial decrease in adaptive potential. In the long term, the better masking of recessive deleterious mutations associated with polyploidy compensates for the initial decrease in additive variance. The time for the tetraploid populations to reach or exceed the additive variance of their diploid progenitors is generally lower than 200 generations. These results highlight that polyploidization per se has a negligible negative effect on the adaptive potential of populations in the short term, and a substantial positive effect in the long term.