The molten-salt tubular absorber/reformer (MoSTAR) project aims to develop a novel type of “double-walled” tubular absorber/reformer with molten-salt thermal storage at high temperature for use in solar natural-gas reforming and solar air receiver, and to demonstrate its performances on the sun with a 5 kWt dish-type solar concentrator. The new concept of double-walled reactor tubes is proposed for use in a solar reformer by Niigata University, Japan, and involves packing a molten/ceramic composite material in the annular region between the internal catalyst tube and the exterior solar absorber wall. This solar tubular absorber concept may be also applied to solar air receiver for solar thermal power generation. The MoSTAR project includes the development of molten-salt thermal storage media, the new design and the fabrication of absorber/reformer with the double-walled absorber tubes, and finally the solar demonstration on the 5 kWt dish concentrator of Inha University in Korea. In this paper, thermal storage media of the series of Na2CO3–MgO composite materials were tested in a double-walled reformer tube with a thermal storage capacity of about 0.3 kWh. The chemical reaction performances for dry reforming of methane during cooling or heat-discharge mode of the reactor tube were investigated using an electric furnace. The experimental results obtained under feed gas mixture of CH4/CO2=1:3 at a residence time of 0.3 s and at 1 atm showed that the single reactor tube with 90 wt % Na2CO3/10 wt % MgO composite material successfully maintained a high methane conversion above 90% with about 0.9 kW reforming scale based on high heating value during 45 min of the heat-discharge mode. The chemical reaction performances of the reactor tube were investigated also for the solar-simulating operation mode. The application of the new reactor tubes to solar tubular reformers is expected to help realize stable operation of the solar reforming process under fluctuating insolation during a cloud passage.