Dose assessment on the lunar surface is important for future long-term crewed activity. In addition to the major radiation of energetic charged particles from galactic cosmic rays (GCRs), neutrons and gamma-rays are generated by nuclear interactions of space radiation with the Moon’s surface materials, as well as natural radioactive nuclides. We obtained neutron and gamma-ray ambient dose distributions on the Moon using Geant4 Monte Carlo simulations combined with the Kaguya gamma-ray spectrometer measurement dataset from February 10 to May 28, 2009. The neutron and gamma-ray dose rates varied in the ranges of 58.7–71.5 mSv/year and 3.33–3.76 mSv/year, respectively, depending on the lunar geological features. The lunar neutron dose was high in the basalt-rich mare, where the iron- and titanium-rich regions are present, due to their large average atomic mass. As expected, the lunar gamma-ray dose map was similar to the distribution of natural radioactive elements (238U, 232Th, and 40K), although the GCR-induced secondary gamma-ray dose was significant at ~ 3.4 mSv/year. The lunar secondary dose contribution resulted in an additional dose of 12–15% to the primary GCR particles. Global dose distributions on the lunar surface will help identify better locations for long-term stays and suggest radiation protection strategies for future crewed missions.