Single-cell RNA-sequencing data generated by a variety of technologies, such as Drop-seq and SMART-seq, can reveal simultaneously the mRNA transcript levels of thousands of genes in thousands of cells. It is often important to identify informative genes or cell-type-discriminative markers to reduce dimensionality and achieve informative cell typing results. We present an ab initio method that performs unsupervised marker selection by identifying genes that have subpopulation-discriminative expression levels and are co- or mutually-exclusively expressed with other genes. Consistent improvements in cell-type classification and biologically meaningful marker selection are achieved by applying SCMarker on various datasets in multiple tissue types, followed by a variety of clustering algorithms. The source code of SCMarker is publicly available at https://github.com/KChen-lab/SCMarker.