Clustering analysis is an important technique for gene expression data analysis. It groups the data according to similar gene expression patterns to explore the unknown gene functions. In recent years, RNA-seq technology has been widely adopted to measure gene expression. It produces a large number of read data, which provide possibilities for clustering analysis of gene expression. In this area, read counts are popularly modeled by the negative binomial distribution to reduce the impact of the non-uniform read distribution, while most existing clustering methods process directly read counts. They donot fully consider the various noise existing in the data, and the uncertainty of gene expression measurements. Some methods also ignore the variability of clustering centers. This study proposes PUseqClust (propagating uncertainty into RNA-Seq clustering) framework for clustering of RNA-seq data. This framework first uses PGSeq to model the stochastic process of read generation. Laplace method is next used to consider correlation between expressions under various conditions and replicates to obtain the uncertainty of expression estimation. Finally, the method adopts the student's t mixture model to perform gene expression clustering. Results show that the proposed methods obtained more biologically relevant clustering results.