The formation and stabilization of telomeric quadruplexes has been shown to inhibit the activity of telomerase, thus establishing telomeric DNA quadruplex as an attractive target for cancer therapeutic intervention. In this context, telomestatin, a G-quadruplex-specific ligand known to bind and stabilize G-quadruplex, is of great interest. Knowledge of the three-dimensional structure of telomeric quadruplex and its complex with telomestatin in solution is a prerequisite for structure-based rational drug design. Here, we report the relative stabilities of human telomeric quadruplex (AG3[T2AG3]3) structures under K+ ion conditions and their binding interaction with telomestatin, as determined by molecular dynamics simulations followed by energy calculations. The energetics study shows that, in the presence of K+ ions, mixed hybrid-type Tel-22 quadruplex conformations are more stable than other conformations. The binding free energy for quadruplex-telomestatin interactions suggests that 1:2 binding is favored over 1:1 binding. To further substantiate our results, we also calculated the change in solvent-accessible surface area (DeltaSASA) and heat capacity (DeltaCp) associated with 1:1 and 1:2 binding modes. The extensive investigation performed for quadruplex-telomestatin interaction will assist in understanding the parameters influencing the quadruplex-ligand interaction and will serve as a platform for rational drug design.