When species hybridize, offspring typically exhibit reduced fitness and maladapted phenotypes. This situation has biosafety implications regarding the unintended spread of novel transgenes, and risk assessments of crop-wild hybrids often assume that poorly adapted hybrid progeny will not evolve adaptive phenotypes. We explored the evolutionary potential of early generation hybrids using nontransgenic wild and cultivated radish (Raphanus raphanistrum, Raphanus sativus) as a model system. We imposed four generations of selection for two weedy traits v early flowering or large size v and measured responses in a common garden in Michigan, USA. Under selection for early flowering, hybrids evolved to flower as early as wild lineages, which changed little. These early-flowering hybrids also recovered wild-type pollen fertility, suggesting a genetic correlation that could accelerate the loss of crop traits when a short life cycle is advantageous. Under selection for large size at reproduction, hybrids evolved longer leaves faster than wild lineages, a potentially advantageous phenotype under longer growing seasons. Although early generation hybrid offspring have reduced fitness, our findings provide novel support for rapid adaptation in crop-wild hybrid populations. Biosafety risk assessment programs should consider the possibility of rapid evolution of weedy traits from early generations of seemingly unfit crop-wild hybrids.