Faithful DNA replication is essential for genome stability. To ensure accurate replication, numerous complex and redundant replication and repair mechanisms function in tandem with the core replication proteins to ensure DNA replication continues even when replication challenges are present that could impede progression of the replication fork. A unique topological challenge to the replication machinery is posed by RNA–DNA hybrids, commonly referred to as R-loops. Although R-loops play important roles in gene expression and recombination at immunoglobulin sites, their persistence is thought to interfere with DNA replication by slowing or impeding replication fork progression. Therefore, it is of interest to identify DNA-associated enzymes that help resolve replication-impeding R-loops. Here, using DNA fiber analysis, we demonstrate that human ribonuclease H1 (RNH1) plays an important role in replication fork movement in the mammalian nucleus by resolving R-loops. We found that RNH1 depletion results in accumulation of RNA–DNA hybrids, slowing of replication forks, and increased DNA damage. Our data uncovered a role for RNH1 in global DNA replication in the mammalian nucleus. Because accumulation of RNA–DNA hybrids is linked to various human cancers and neurodegenerative disorders, our study raises the possibility that replication fork progression might be impeded, adding to increased genomic instability and contributing to disease.