JAEA (Japan Atomic Energy Agency) has conducted feasibility studies of the fuel and of the reactor core for the plutonium-burner HTGR (High Temperature Gas-cooled Reactor). The increase of the internal pressure, which is caused by generations of CO gas and stable noble gases, is considered to be the one of the major causes of TRISO (TRI-structural ISO-tropic) fuel failure at high burn-up. The CO gas is generated by the chemical reaction of the graphite making up the buffer layer with the free-oxygen released from the fuel kernel by fission. The stable noble gases, which are fission products, are also released from the fuel kernel. Although it is considered very difficult to suppress the increase of the partial pressure of the stable noble gases because of its chemically inert nature, the increase of the CO gas partial pressure can be suppressed by reducing the free-oxygen mole concentration using a chemical reaction. ZrC acts an oxygen getter, which reduces the free-oxygen generated with fission reaction. An increase of the CO gas partial pressure with burn-up in a TRISO fuel is expected to be suppressed by coating ZrC on a fuel kernel. A PuO2-YSZ (Yttria Stabilized Zirconia) fuel kernel with a ZrC coating, which enhances safety, security and safeguard, namely: 3S-TRISO fuel, was proposed to introduce to the plutonium-burner HTGR. In this study, the efficiency of the ZrC coating as the free-oxygen getter under a HTGR temperature condition was examined based on a thermochemical calculation. A preliminary feasibility study on the 3S-TRISO fuel that enables to attain a high burn-up around 500 GWd/t was also conducted focusing on a fuel failure caused by an increase of the internal pressure. Additionally, a preliminary nuclear analysis was conducted for the plutonium-burner HTGR with a fuel shuffling in the radial direction. As a result, the thermochemical calculation result showed that all the amount of the free-oxygen is captured by a thin ZrC coating under 1600 degrees C condition. The plutonium-burner HTGR will be designed to suppress fuel temperature to be lower than 1600 degrees C under severe accident conditions, and hence it was confirmed that coating ZrC on the fuel kernel is very effective method to suppress the internal pressure. The internal pressure the 3S-TRISO fuel at 500 GWd/t is calculated to be lower than 60 MPa, which allows to prevent the fuel failure, and hence the feasibility of the 3S-TRISO fuel was also confirmed. Additionally, the results of the whole core burn-up calculations showed that the fuel shuffling in the radial direction allows to achieve the high burn-up around 500 GWd/t. It also showed that the temperature coefficient of reactivity is negative value during the rated power condition through the operation period.