We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and β-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and β-hairpin configurations of model peptides, varying Morse potential parameters, the hydrophobicities of residue side chains, and pH, which determines the charges of residue side chains. We construct a model triblock polypeptide mimicking the sequence of residues α-synuclein at two different pHs. The conformations of this model polypeptide depend on pH similarly to the behavior observed experimentally. The suggested approach to accounting for hydrogen bond formation within the general DPD framework may make the DPD method a competitive alternative to CGMD for modeling equilibrium and dynamic properties of proteins and polypeptides, especially during their transport in confined environments.