Cellular differentiation is a complex process where a less specialized cell evolves into a more specialized cell. Despite the increasing research effort, identification of cell-fate determinants (transcription factors (TFs) determining cell fates during differentiation) still remains a challenge, especially when closely related cell types from a common progenitor are considered. Here, we develop SeesawPred, a web application that, based on a gene regulatory network (GRN) model of cell differentiation, can computationally predict cell-fate determinants from transcriptomics data. Unlike previous approaches, it allows the user to upload gene expression data and does not rely on pre-compiled reference data sets, enabling its application to novel differentiation systems. SeesawPred correctly predicted known cell-fate determinants on various cell differentiation examples in both mouse and human, and also performed better compared to state-of-the-art methods. The application is freely available for academic, non-profit use at http://seesaw.lcsb.uni.lu.