Radiation shielding calculations were performed for the shielding design around beam injection and beam extraction areas at the 3-GeV proton synchrotron in the Japan Proton Accelerator Research Complex (J-PARC) with the PHITS Monte Carlo code. Prompt dose rates outside the shields were obtained from calculated neutron energy spectra and flux-to-dose conversion coefficients prepared for the shielding design in J-PARC. The thicknesses of shields were determined from the comparison results of the prompt dose rates with the criteria of dose limit for the design in J-PARC.