A computational method for the radiological characterization of the Greek Research Reactor (GRR-1) core supporting grid plate is presented. It is based on three-dimensional Monte Carlo neutron and photon transport simulations, analytical radionuclide inventory calculations, and measured gamma dose rates. The spatial distribution of neutron fluxes and spectra were derived by an implicit MCNP reactor core model. The radionuclide inventory was estimated using the FISPACT code. The associated source term was included in an accurate MCNP model of the grid plate assembly deriving the resulting gamma dose rates. The dominant gamma dose-producing nuclide was 60Co generated by activation of cobalt impurity in the stainless steel parts. The cobalt impurity concentration in the stainless steel parts was determined on the basis of best agreement between gamma dose rate calculations and measurements. The specific activity of grid plate components was evaluated as a function of cooling time after reactor shutdown. The proposed methodology provides a useful tool for work planning, control of occupational exposure and waste management during reactor renovation, and maintenance or decommissioning activities.