Understanding cell differentiation-the process of generation of distinct cell-types-plays a pivotal role in developmental and evolutionary biology. Transcriptomic information and epigenetic marks are useful to elucidate hierarchical developmental relationships among cell-types. Standard phylogenetic approaches such as maximum parsimony, maximum likelihood and neighbor joining have previously been applied to ChIP-Seq histone modification data to infer cell-type trees, showing how diverse types of cells are related. In this study, we demonstrate the applicability and suitability of quartet-based phylogenetic tree estimation techniques for constructing cell-type trees. We propose two quartet-based pipelines for constructing cell phylogeny. Our methods were assessed for their validity in inferring hierarchical differentiation processes of various cell-types in H3K4me3, H3K27me3, H3K36me3, and H3K27ac histone mark data. We also propose a robust metric for evaluating cell-type trees.