The class B glucagon-like peptide-1 (GLP-1) G protein-coupled receptor is a major target for the treatment of type 2 diabetes and obesity. Endogenous and mimetic GLP-1 peptides exhibit biased agonism - a difference in functional selectivity - that may provide improved therapeutic outcomes. Here we describe the structure of the human GLP-1 receptor in complex with the G protein-biased peptide exendin-P5 and a Gα(s) heterotrimer, determined at a global resolution of 3.3 Å. At the extracellular surface, the organization of extracellular loop 3 and proximal transmembrane segments differs between our exendin-P5-bound structure and previous GLP-1-bound GLP-1 receptor structure. At the intracellular face, there was a six-degree difference in the angle of the Gαs-α5 helix engagement between structures, which was propagated across the G protein heterotrimer. In addition, the structures differed in the rate and extent of conformational reorganization of the Gα(s) protein. Our structure provides insights into the molecular basis of biased agonism.