A female's mate preference is a potentially complex function relating variation in multiple male phenotypes with her probability of accepting individual males as a mate. Estimating the quantitative genetic basis preference functions within a population is empirically challenging yet key to understanding preference evolution. We employed a recently described approach that uses random-coefficient mixed models in the analysis of function-valued traits. Using a half-sibling breeding design in a laboratory-adapted Drosophila serrata population, we estimated the genetic (co)variance function of female preference for male sexual displays composed of nine contact pheromones. The breeding design was performed across two environments: the food to which the population was well adapted and a novel food that reduced average female productivity by 35%. Significant genetic variance in female preference was detected and the majority (64.2%) was attributable to a single genetic dimension (eigenfunction), suggesting that preferences for different pheromones are not genetically independent. The second eigenfunction, accounting for 24% of the total genetic variance, approached significance in a conservative test, suggesting the existence of a second, independent genetic dimension. There was no evidence that the genetic basis of female preference differed between the two environments, suggesting the absence of genotype-by-environment interactions and hence a lack of condition-dependent preference expression.