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While single-cell RNA sequencing (scRNA-seq) allows researchers to analyze gene expression in individual cells, its unique characteristics like over-dispersion, zero-inflation, high gene-gene correlation, and large data volume with many features pose challenges for most existing feature selection methods. In this paper, we present a feature selection method based on neural network (scFSNN) to solve classification problem for the scRNA-seq data. scFSNN is an embedded method that can automatically select features (genes) during model training, control the false discovery rate of selected features and adaptively determine the number of features to be eliminated. Extensive simulation and real data studies demonstrate its excellent feature selection ability and predictive performance.