Reversible foldings of a beta-hairpin peptide, chignolin, by recently invented hybrid Hamiltonian replica exchange molecular dynamics simulations based on Poisson-Boltzmann model in explicit water are demonstrated. Initiated from extended structures the peptide folded and unfolded a couple of times in seven out of eight replica trajectories during 100 nanoseconds simulation. The folded states have the lowest all-atom root mean squared deviation of 1.3 A with respect to the NMR structures. At T=300 K the occurrence of folded states was converged to 62% during 80 ns simulation which agrees well with experimental data. Especially, a detailed structural evolution map was constructed based on 800,000 structural snapshots and from where a unique folding doorway emerges. Compared with 130 ns standard replica exchange simulation using 24 replicas on the same system, the hybrid Hamiltonian replica exchange molecular dynamics simulation presents consistent results.