One possibility for why individual differences in behavioral plasticity are frequently associated with differences in personality might be that variation in personality is functionally related to variation in cognition. Evidence supporting a link between personality and cognition, however, is still limited and contradictory. In this study, we then conducted a laboratory experiment with zebra finches (Taeniopygia guttata) aimed at examining the role of cognition in shaping individual differences in contextual plasticity (i.e., plasticity in behavior between contexts). Specifically, we measured neophobia by quantifying the latency of the birds to eat near a novel object in two different environments across a social gradient and assessed their learning performance on two discriminant tasks and a reversal task. In agreement with our expectation, we found that less neophobic individuals were less plastic in their responses compared to more neophobic ones. Less neophobic individuals were also faster to reach the learning criterion but only in the less difficult discriminant task they performed first. On the contrary, although we found evidence for individual consistency in learning performances, differences among individuals in the number of trials needed to pass the task in both the more difficult discriminant and reversal tasks were not associated with individual differences in neophobia. Thus, our findings indicate that individual differences in contextual plasticity do not necessarily result from some individuals being more sensitive to environmental changes. Instead, we suggest that differences among individuals in their level of plasticity might result from differences in the number of suitable habitats they may occupy.