Dynamic changes of gene expression reflect an intrinsic mechanism of how an organism responds to developmental and environmental signals. With the increasing availability of expression data across a time-space scale by RNA-seq, the classification of genes as per their biological function using RNA-seq data has become one of the most significant challenges in contemporary biology. Here we develop a clustering mixture model to discover distinct groups of genes expressed during a period of organ development. By integrating the density function of multivariate Poisson distribution, the model accommodates the discrete property of read counts characteristic of RNA-seq data. The temporal dependence of gene expression is modeled by the first-order autoregressive process. The model is implemented with the Expectation-Maximization algorithm and model selection to determine the optimal number of gene clusters and obtain the estimates of Poisson parameters that describe the pattern of time-dependent expression of genes from each cluster. The model has been demonstrated by analyzing a real data from an experiment aimed to link the pattern of gene expression to catkin development in white poplar. The usefulness of the model has been validated through computer simulation. The model provides a valuable tool for clustering RNA-seq data, facilitating our global view of expression dynamics and understanding of gene regulation mechanisms. 