A Very High Temperature Reactor (VHTR) is a next generation nuclear reactor system. From the view point of the safety characteristic, the passive cooling system should be designed for the VHTR as the best way of reactor vessel cooling system (VCS). Therefore, the gas cooling system with natural circulation is considered as a candidate for the VCS of the VHTR. Japan Atomic Energy Agency (JAEA) is advancing the technology development of the VHTR using the HTTR and is now pursuing design and development of commercial systems such as the 300MWe gas turbine high temperature reactor GTHTR300C (Gas Turbine High Temperature Reactor 300 for Cogeneration). The objective of this study is to investigate the heat transfer characteristics by natural convection in the vertical rectangular channel inserting the porous materials with high porosity. It is also to examine heat transfer characteristics of one side heated vertical rectangular channel with natural circulation in order to construct the passive cooling system of the VHTR. This paper describes the heat transfer coefficient and the amount of the removed heat in the proposed channel. In order to enhance the heat transfer, a porous material was inserted into the channel with high porosity. In order to apply to the VHTR such as GTHTR300C, it is necessary to perform a design study of the passive cooling system. This study is to refer to make design of the passive cooling system for the VCS.