Given the evolution of High-Temperature Gas-cooled Reactor(HTGR) designs, the source terms for licensing must be developed. There are three potential source terms: fission products, actinides in the fuel and tritium in the coolant. It is necessary to provide first an inventory of the source terms under normal operations. An analysis of source terms has yet to be performed for HTGRs. The previous code, which can estimate the inventory of the source terms for LWRs, cannot be used for HTGRs because the general data of a typical neutron cross-section and flux has not been developed. Thus, this paper uses a combination of the MCNP, ORIGEN, and MONTETEBURNS codes for an estimation of the source terms. A method in which the HTR-10 core is constructed using the unit lattice of a body-centered cubic is developed for core modeling. Based on this modeling method by MCNP, the generation of fission products, actinides and tritium with an increase in the burnup ratio is simulated. The model developed by MCNP appears feasible through a comparison with models developed in previous studies. Continuous fuel management is divided into five periods for the feeding and discharging of fuel pebbles. This discrete fuel management scheme is employed using the MONTEBURNS code. Finally, the work is investigated for 22 isotope fission products of nuclides, 22 actinides in the core, and tritium in the coolant. The activities are mainly distributed within the range of $10^{15}{sim}10^{17}$ Bq in the equilibrium core of HTR-10. The results appear to be highly probable, and they would be informative when the spent fuel of HTGRs is taken into account. The tritium inventory in the primary coolant is also taken into account without a helium purification system. This article can lay a foundation for future work on analyses of source terms as a platform for safety assessment in HTGRs.