The melting transition of Ga and In was measured by using a nW-stabilized differential scanning calorimeter working in a magnetic bore. The magnetic effect on the thermometer was about 18 mK at 5 T, which was corrected for the measurement of the magnetic effect on the melting transition of Ga and In. The melting temperatures of Ga and In with the magnetic field of 5 T were obtained to be 8.3 and 10.2 mK, respectively higher than those without the magnetic field. These results show that the solid phase to be relatively more stable under the magnetic field. The calculated temperature shifts of the melting transition due to the magnetic field using the magneto-Clapeyron equation and the reference data of magnetic susceptibility were negative values for both Ga and In, being contradictory to the experimental results.