Dropout is a common phenomenon in single-cell RNA-seq (scRNA-seq) data, and when left unaddressed affects the validity of the statistical analyses. Despite this, few current methods for differential expression (DE) analysis of scRNA-seq data explicitly model the dropout process. We develop DECENT, a DE method for scRNA-seq data that explicitly models the dropout process and performs statistical analyses on the inferred pre-dropout counts. We demonstrate using simulated and real datasets the superior performance of DECENT compared to existing methods. DECENT does not require spike-in data, but spike-ins can be used to improve performance when available. The method is implemented in a publicly-available R package.