Abstract Single cell RNA-seq data allows insight into normal cellular function and diseases including cancer through the molecular characterisation of cellular state at the single-cell level. Dimensionality reduction of such high-dimensional datasets is essential for visualization and analysis, but single-cell RNA-seq data is challenging for classical dimensionality reduction methods because of the prevalence of dropout events leading to zero-inflated data. Here we develop a dimensionality reduction method, (Z)ero (I)nflated (F)actor (A)nalysis (ZIFA), which explicitly models the dropout characteristics, and show that it improves modelling accuracy on simulated and biological datasets.