Allosaurus is one of the most common Mesozoic theropod dinosaurs. We present a histological analysis to assess its growth strategy and ontogenetic limb bone scaling. Based on an ontogenetic series of humeral, ulnar, femoral, and tibial sections of fibrolamellar bone, we estimate the ages of the largest individuals in the sample to be between 13-19 years. Growth curve reconstruction suggests that maximum growth occurred at 15 years, when body mass increased 148 kg/year. Based on larger bones of Allosaurus, we estimate an upper age limit of between 22-28 years of age, which is similar to preliminary data for other large theropods. Both Model I and Model II regression analyses suggest that relative to the length of the femur, the lengths of the humerus, ulna, and tibia increase in length more slowly than isometry predicts. That pattern of limb scaling in Allosaurus is similar to those in other large theropods such as the tyrannosaurids. Phylogenetic optimization suggests that large theropods independently evolved reduced humeral, ulnar, and tibial lengths by a phyletic reduction in longitudinal growth relative to the femur.