In mammals and seed plants, a subset of genes is regulated by genomic imprinting where an allele's activity depends on its parental origin. The parental conflict theory suggests that genomic imprinting evolved after the emergence of an embryo-nourishing tissue (placenta and endosperm), resulting in an intragenomic parental conflict over the allocation of nutrients from mother to offspring. It was predicted that imprinted genes, which arose through antagonistic co-evolution driven by a parental conflict, should be subject to positive darwinian selection. Here we show that the imprinted plant gene MEDEA (MEA), which is essential for seed development, originated during a whole-genome duplication 35 to 85 million years ago. After duplication, MEA underwent positive darwinian selection consistent with neo-functionalization and the parental conflict theory. MEA continues to evolve rapidly in the out-crossing species Arabidopsis lyrata but not in the self-fertilizing species Arabidopsis thaliana, where parental conflicts are reduced. The paralogue of MEA, SWINGER (SWN; also called EZA1), is not imprinted and evolved under strong purifying selection because it probably retained the ancestral function of the common precursor gene. The evolution of MEA suggests a late origin of genomic imprinting within the Brassicaceae, whereas imprinting is thought to have originated early within the mammalian lineage.