Guanine-rich nucleic acid sequences challenge the replication, transcription, and translation machinery by spontaneously folding into G-quadruplexes, the unfolding of which requires forces greater than most polymerases can exert(1,2). Eukaryotic cells contain numerous helicases that can unfold G-quadruplexes(3). The molecular basis of the recognition and unfolding of G-quadruplexes by helicases remains poorly understood. DHX36 (also known as RHAU and G4R1), a member of the DEAH/RHA family of helicases, binds both DNA and RNA G-quadruplexes with extremely high affinity(4-6), is consistently found bound to G-quadruplexes in and is a major source of G-quadruplex unfolding activity in HeLa cell lysates(6). DHX36 is a multi-functional helicase that has been implicated in G-quadruplex-mediated transcriptional and post transcriptional regulation, and is essential for heart development, haematopoiesis, and embryogenesis in mice(9-12). Here we report the co-crystal structure of bovine DHX36 bound to a DNA with a G-quadruplex and a 3' single-stranded DNA segment. We show that the N-terminal DHX36-specific motif folds into a DNA binding-induced alpha-helix that, together with the OB-fold-like subdomain, selectively binds parallel G-quadruplexes. Comparison with unliganded and ATP-analogue-bound DHX36 structures, together with single-molecule fluorescence resonance energy transfer (FRET) analysis, suggests that G-quadruplex binding alone induces rearrangements of the helicase core; by pulling on the single-stranded DNA tail, these rearrangements drive G-quadruplex unfolding one residue at a time.