The class B glucagon-like peptide-1 (GLP-1) G protein-coupled receptor is a major therapeutic target for treatment of type 2 diabetes and obesity. Endogenous and mimetic GLP-1 peptides exhibit biased agonism that may provide therapeutic differentiation. Here we report the structure of human GLP-1 receptor in complex with the G protein-biased peptide, exendin-P5, and Gαs heterotrimer determined at 3.3 Å global resolution. At the extracellular face of the receptor, there was a distinct organisation of extracellular loop 3 and proximal transmembrane segments, which differ between the exendin-P5 structure and the published GLP-1 bound GLP-1 receptor. At the intracellular face, there was a 6-degree difference in the angle of the Gas-a5 helix engagement between the receptors that was propagated across the G protein heterotrimer, and differences in the rate and extent of conformational reorganisation of the Gαs protein. This new structure provides novel insights into the structural basis of biased agonism.