Certain events of low probability that occur in material systems have a considerable impact on system characterization. Though rare event simulation has been a well-researched problem in areas like financial risk assessment and communication systems, modeling and simulation of rare events in material systems remain under-explored.In this paper, we turn to large deviations theory and importance sampling to develop a solution to simulate an important rare event that arises in polycrystalline materials. More specifically, the microstructure of a polycrystalline material consists of grains that have different orientations associated with them. These grains evolve over time and this phenomenon is called grain growth. The growth of grains is a slow process, making direct observation expensive and impractical. To alleviate this problem, computational methods have been developed to simulate grain growth. However, one event of interest which occurs with low probability involves a single grain that grows abnormally large at the expense of other grains. Though Gibbs distribution based models exist for such abnormal grain growth, occurrence of this event under such models is still rare enough that we still need to draw many samples before an abnormal growth manifests.We propose an importance sampling distribution from which to draw samples to simulate abnormal grain growth, instead of the conventional Gibbs distribution used to model grain growth. Our proposed importance sampling distribution is based on an asymptotically efficient rare event probability estimator. With our method, we consistently generate abnormal grain growth, thus providing a reliable solution to this important materials science problem. Our solution can potentially be used in general to simulate rare events in any system that is modeled by a Gibbs distribution.