Clustering is a prevalent analytical means to analyze single cell RNA sequencing (scRNA-seq) data but the rapidly expanding data volume can make this process computationally challenging. New methods for both accurate and efficient clustering are of pressing need. Here we proposed Spearman subsampling-clustering-classification (SSCC), a new clustering framework based on random projection and feature construction, for large-scale scRNA-seq data. SSCC greatly improves clustering accuracy, robustness, and computational efficacy for various state-of-the-art algorithms benchmarked on multiple real datasets. On a dataset with 68,578 human blood cells, SSCC achieved 20% improvement for clustering accuracy and 50-fold acceleration, but only consumed 66% memory usage, compared to the widelyused software package SC3. Compared to k-means, the accuracy improvement of SSCC can reach 3-fold. An R implementation of SSCC is available at https://github.com/Japrin/sscClust. Keywords: Classification; Clustering; RNA-seq; Single cell; Subsampling.