Many variants of language models have been proposed for information retrieval. Most existing models are based on multinomial distribution and would score documents based on query likelihood computed based on a query generation probabilistic model. In this paper, we propose and study a new family of query generation models based on Poisson distribution. We show that while in their simplest forms, the new family of models and the existing multinomial models are equivalent. However, based on different smoothing methods, the two families of models behave differently. We show that the Poisson model has several advantages, including naturally accommodating per-term smoothing and modeling accurate background more efficiently. We present several variants of the new model corresponding to different smoothing methods, and evaluate them on four representative TREC test collections. The results show that while their basic models perform comparably, the Poisson model can out perform multinomial model with per-term smoothing. The performance can be further improved with two-stage smoothing.