Large amounts of fission products (FP) were released at the Fukushima Daiichi Nuclear Power Plant of Tokyo Electricity Power Company due to the accident, initiated by the tsunami that was triggered by the East Japan Great Earthquake on March 11, 2011. It has been more than five years since the disaster occurred. The radioactivity owing to FP deposited on the grounds, houses, forests and so on have been decreasing steadily by the decay of FP, soil infiltration, weathering effect and the planned decontamination. As a result, the residence restriction areas have been re-organized as areas prepared for evacuation cancellation and it has been allowed for the residents to return to their homes. The conscious surveys for residents showed that they were worrying about the influence of radioactivity to human body. Therefore, it is necessary to let them know sufficient detailed information and knowledge. The decrease of radiation dose depends considerably on the density of the building construction materials, so that it would be desirable for indoor radiation dose rate to be estimated by taking account of housing types and floor plans. This paper deals with a novel method for calculating radiation dose rate within a building and around its surroundings. We employed the Monte Carlo method to calculate gamma ray penetration through various shield configurations and the absorption within an object positioned at an evaluation point. The gamma rays shifted to lower energy levels caused by the Compton scattering, i.e. buildup fluxes, were simply treated using the buildup factor as a function of the mean free path of photons. RADAR-γ code which has been developed on the basis of this study was benchmarked for a simplified geometry case with Cesium 137 deposited on the ground surface. The results were compared with the point-kernel integration code QAD-CGGP-A, which has been widely used in radiative physics analyses to calculate operational exposures and gamma radiation fields through shielding. The results of both methods were in good agreement. It was confirmed that the proposed method could be used for predicting radiation dose rate in the area where FP have been deposited.