Single cell RNA-seq data, like data from other sequencing technology, contain systematic technical noise. Such noise results from a combined effect of unequal efficiencies in the capturing and counting of mRNA molecules, such as extraction/amplification efficiency and sequencing depth. We show that such technical effects are not only cell-specific, but also affect genes differently, thus a simple cell-wise size factor adjustment may not be sufficient. We present a non-linear normalization approach that provides a cell- and gene-specific normalization factor for each gene in each cell. We show that the proposed normalization method (implemented in “SC2P" package) reduces more technical variation than competing methods, without reducing biological variation. When technical effects such as sequencing depths are not balanced between cell populations, SC2P normalization also removes the bias due to uneven technical noise. This method is applicable to scRNA-seq experiments that do not use unique molecular identifier (UMI) thus retain amplification biases.