We have determined the solution structure of the complex between an arginine-glycine-rich RGG peptide from the human fragile X mental retardation protein (FMRP) and an in vitro-selected guanine-rich (G-rich) sc1 RNA. The bound RNA forms a newly discovered G-quadruplex separated from the flanking duplex stem by a mixed junctional tetrad. The RGG peptide is positioned along the major groove of the RNA duplex, with the G-quadruplex forcing a sharp turn of R(10)GGGGR(15) at the duplex-quadruplex junction. Arg10 and Arg15 form cross-strand specificity-determining intermolecular hydrogen bonds with the major-groove edges of guanines of adjacent Watson-Crick G•C pairs. Filter-binding assays on RNA and peptide mutations identify and validate contributions of peptide-RNA intermolecular contacts and shape complementarity to molecular recognition. These findings on FMRP RGG domain recognition by a combination of G-quadruplex and surrounding RNA sequences have implications for the recognition of other genomic G-rich RNAs.