Background One goal of expression data analysis is to discover the biological significance or function of genes that are differentially expressed. Gene Set Enrichment (GSE) analysis is one of the main tools for function mining that has been widely used. However, every gene expressed in a cell is valuable information for GSE for single-cell RNA sequencing (scRNA-SEQ) data and not should be discarded. Methods We developed the functional expression matrix (FEM) algorithm to utilize the information from all expressed genes. The algorithm converts the gene expression matrix (GEM) into a FEM. The FEM algorithm can provide insight on the biological significance of a single cell. It can also integrate with GEM for downstream analysis. Results We found that FEM performed well with cell clustering and cell-type specific function annotation in three datasets (peripheral blood mononuclear cells, human liver, and human pancreas).