Recently the LNG(liquified natural gas) public buses have been introduced to prevent the air pollution in metropolitan areas. As the LNG temperature in fuel tank is as low as $-162^{circ}C$. the thermal and structural effects of tank components need to be studied for safe introduction in the market. Especially the support system of LNG fuel tank in vehicle, which has connected with inside and outside of tanks, should put attention to reduce the structural stress due to cryogenic temperature and to restrict the heat flux from ambient. There are two supporting systems in the tank, that one is connected between inside and outside tanks by welding, and the other is the inserted support system which is a cylindrical SUS bar inserted in a hole of the supporting plate. In this study the temperature distribution and thermal stress of the inserted support system were evaluated by using the utility program as ANSYS. The results showed that the rate of heat transfer to inner tank through this support system was quite small due to limited contact of support bar with plate. but the thermal stress of support plate was obtained beyond the limited tensile value of SUS304. The cautious design for the support plate part, therefore, should be given to make the safe support system of LNG vehicle fuel tank.