Gene fusions can play important roles in tumor initiation and progression. While fusion detection so far has been from bulk samples, full-length single-cell RNA sequencing (scRNA-seq) offers the possibility of detecting gene fusions at the single-cell level. However, scRNA-seq data have a high noise level and contain various technical artifacts that can lead to spurious fusion discoveries. Here, we present a computational tool, scFusion, for gene fusion detection based on scRNA-seq. We evaluate the performance of scFusion using simulated and five real scRNA-seq datasets and find that scFusion can efficiently and sensitively detect fusions with a low false discovery rate. In a T cell dataset, scFusion detects the invariant TCR gene recombinations in mucosal-associated invariant T cells that many methods developed for bulk data fail to detect; in a multiple myeloma dataset, scFusion detects the known recurrent fusion IgH-WHSC1, which is associated with overexpression of the WHSC1 oncogene. Our results demonstrate that scFusion can be used to investigate cellular heterogeneity of gene fusions and their transcriptional impact at the single-cell level.