We have investigated new folding pathways of human telomeric type-1 and type-2 G-quadruplex conformations via intermediate hairpin and triplex structures. The stabilization energies calculated by ab initio methods evidenced the formation of a hairpin structure with Hoogsteen GG base pairs. Further calculations revealed that the G-triplet is more stable than the hairpin conformation and equally stable when compared to the G-tetrad. This indicated the possibility of a triplex intermediate. The overall folding is facilitated by K+ association in each step, as it decreases the electrostatic repulsion. The K+ binding site was identified by molecular dynamics simulations. We then focused on the syn/anti arrangement and found that the anti conformation of deoxyguanosine is more stable than the syn conformation, which indicated that folding would increase the number of anti conformations. The K+ binding to a hairpin near the second lateral TTA loop was found to be preferable, considering entropic effects. Stacking of G-tetrads with the same conformation (anti/anti or syn/syn) is more stable than mixed stacking (anti/syn and vice versa). These results suggest the formation of type-1 and type-2 G-quadruplex structures with the possibility of hairpin and triplex intermediates.