Adult hippocampal neurogenesis is increased by antidepressants, and is required for some of their behavioral effects. However, it remains unclear whether expanding the population of adult-born neurons is sufficient to affect anxiety and depression-related behavior. Here, we use an inducible transgenic mouse model in which the pro-apoptotic gene Bax is deleted from neural stem cells and their progeny in the adult brain, and thereby increases adult neurogenesis. We find no effects on baseline anxiety and depression-related behavior; however, we find that increasing adult neurogenesis is sufficient to reduce anxiety and depression-related behaviors in mice treated chronically with corticosterone (CORT), a mouse model of stress. Thus, neurogenesis differentially affects behavior under baseline conditions and in a model of chronic stress. Moreover, we find no effect of increased adult hippocampal neurogenesis on hypothalamic-pituitary-adrenal (HPA) axis regulation, either at baseline or following chronic CORT administration, suggesting that increasing adult hippocampal neurogenesis can affect anxiety and depression-related behavior through a mechanism independent of the HPA axis. The use of future techniques to specifically inhibit BAX in the hippocampus could be used to augment adult neurogenesis, and may therefore represent a novel strategy to promote antidepressant-like behavioral effects.