We present experimental studies on ion acceleration using an 800-nm circularly polarized laser pulse with a peak intensity of 6.9×10^{19} W/cm^{2} interacting with an overdense plasma that is produced by a laser prepulse ionizing an initially ultrathin plastic foil. The proton spectra exhibit spectral peaks at energies up to 9 MeV with energy spreads of 30% and fluxes as high as 3×10^{12} protons/MeV/sr. Two-dimensional particle-in-cell simulations reveal that collisionless shocks are efficiently launched by circularly polarized lasers in exploded plasmas, resulting in the acceleration of quasimonoenergetic proton beams. Furthermore, this scheme predicts the generation of quasimonoenergetic proton beams with peak energies of approximately 150 MeV using current laser technology, representing a significant step toward applications such as proton therapy.