We extend the predator-prey model developed by Ackleh et al. (2019) to account for seasonal reproduction. We model the reproduction of prey as a periodic function of period two, representing two seasons: a breeding season and a non-breeding season. We study the dynamics of the model and show that when the inherent reproduction number of the prey and the invasion reproduction number of the predator are larger than one, then the system is permanent and an interior 2-cycle exists and is locally asymptotically stable. We then compare the impact of seasonality on the prey density with and without predator interaction. We show that, while seasonality is always deleterious (resulting in a lower prey density average over a full period) when the predator is not present, it can be advantageous for certain parameter ranges when the predator is present.