It is a significant step for single cell analysis to identify cell types through clustering single-cell RNA sequencing (scRNA-seq) data. However, great challenges still remain due to the inherent high-dimensionality, noise, and sparsity of scRNA-seq data. In this study, scPEDSSC, a deep sparse subspace clustering method based on proximity enhancement, is put forward. The self-expression matrix (SEM), learned from the deep auto-encoder with two part generalized gamma (TPGG) distribution, are adopted to generate the similarity matrix along with its second power. Compared with eight state-of-the-art single-cell clustering methods on twelve real biological datasets, the proposed method scPEDSSC can achieve superior performance in most datasets, which has been verified through a number of experiments.