Since an ignited deuterium-tritium plasma of a moving ring compact torus reactor (MRCTR) is thermally unstable at the operating temperature, suppression of the thermal instability is an essential issue for maintaining the stationary burning of a plasma. The feedback stabilization by means of major radial compression-decompression is proposed for a burn control in an MRCTR. The compression-decompression is carried out through the regulation of the solenoidal magnetic field according to the deviation of the ion temperature from the equilibrium value. The dynamics of a plasma core with a feedback control is calculated in a zero-dimensional plasma model assuming the empirical confinement scalings obtained in the present tokamak experiments. The effects of ion density on the dynamics are also studied for two extreme cases of complete particle recycling and perfect pumping. The scheme is found to be effective for the burn control. The deviations of a major radius and a fusion output power are less than several percents of the equilibrium values during the control to suppress the temperature excursion. The rate of change in the magnetic field for the control is as slow as 500 G/s.