G-quadruplex DNA (GqDNA) structures play an important role in many specific cellular functions and are promising anti-tumor targets for small molecules (ligands). Here, we measured the dynamic Stokes shift of a ligand (Hoechst) bound to parallel c-Myc (mPu22) GqDNA over five decades of time from 100 fs to 10 ns, and compared it with the previously reported dynamics of DAPI bound to antiparallel human telomeric (hTelo22) GqDNA (Pal et al 2015 J. Phys. Chem. Lett. 6 1754). Stokes shift data from fluorescence up-conversion and time-correlated single photon counting experiments was combined to cover the broad dynamic range. The results show that the solvation dynamics of Hoechst in parallel mPu22 GqDNA follow a power law relaxation, added to fast 2 ps exponential relaxation, from 100 fs to 10 ns, with only a subtle difference of power law exponents in the two ligand-GqDNA systems (0.06 in Hoechst-mPu22 compared to 0.16 in DAPI-hTelo22). We measured steady-state fluorescence spectra and time-resolved anisotropy decays which confirm the tight binding of Hoechst to parallel mPu22 with a binding constant of ~1 × 10 M. The molecular docking of Hoechst in parallel GqDNA followed by a 50 ns molecular dynamics (MD) simulation on a Hoechst-GqDNA complex reveals that Hoechst binds to one of the outer G-tetrads by end-stacking near G13 and G4, which is different from the binding site of DAPI inside a groove of antiparallel hTelo22 GqDNA. Reconciling previous experimental and simulation results, we assign the 2 ps component to the hydration dynamics of only weakly perturbed water near mPu22 and the power law relaxation to the coupled motion of water and DNA (i.e. DNA backbone, unpaired bases and loops connecting G-tetrads) which come near the Hoechst inside parallel GqDNA.