The glucagon-like peptide-1 receptor (GLP-1R) is a well-known target of therapeutics industries for the treatment of various metabolic diseases like type 2 diabetes and obesity. The structural-functional relationships of small molecule agonists and GLP-1R are yet to be understood. Therefore, an attempt was made on structurally known GLP-1R agonists (Compound 1, Compound 2, Compound A, Compound B, and (S)-8) to study their interaction with the extracellular domain of GLP-1R. In this study, we explored the dynamics, intrinsic stability, and binding mechanisms of these molecules through computational modeling, docking, molecular dynamics (MD) simulations and molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) binding free energy estimation. Molecular docking study depicted that hydrophobic interaction (pi-pi stacking) plays a crucial role in maintaining the stability of the complex, which was also supported by intermolecular analysis from MD simulation study. Principal component analysis suggested that the terminal ends along with the turns/loops connecting adjacent helix and strands exhibit a comparatively higher movement of main chain atoms in most of the complexes. MM/PBSA binding free energy study revealed that non-polar solvation (van der Waals and electrostatic) energy subsidizes significantly to the total binding energy, and the polar solvation energy opposes the binding agonists to GLP-1R. Overall, we provide structural features information about GLP-1R complexes that would be conducive for the discovery of new GLP-1R agonists in the future for the treatment of various metabolic diseases. Communicated by Ramaswamy H. Sarma.