Experimental hardware has been developed to perform the experiments of drop Marangoni migration in the case of intermediate Reynolds numbers ina microgravity environment. The experiments were completed using the drop shaft free fall facility with a 4.5 s microgravity period in the Microgravity Laboratory of Japan. A special experimental method was designed for experimenting with a short microgravity period. In this experiment, the thermocapillary velocity of drop migration, driven only by the thermocapillary effect, was obtained. Experimental results show that Marangoni migration velocity depends on the temperature gradient and the drop diameter For fixed experimental mediums; the thermocapillary velocity of this present experiment is obviously smaller than the one suggested by YGB linear theory. This conclusion agrees, in general, with that of the ground-based experiment.