It is well known that diurnal cycle of precipitation and convective activity over tropical coastal waters is characterized by offshore-ward migration of areas with large precipitation during nighttime and early morning from near the coast to sometimes several hundred kilometers. With one of the aims being to observe this phenomenon, we conducted an intensive observation campaign in the western coastal area of Sumatra Island, Indonesia, in the 2017/18 boreal winter, named YMC-Sumatra 2017, where YMC stands for “the Years of the Maritime Continent.” As a part of the campaign, we deploy the Research Vessel Mirai at about 90 km off the coast to perform a variety of observations including 3-hourly radiosonde and continuous weather radar observations. This study analyzes these observations for the 27-day period of 5-31 December 2017 to examine environmental conditions of the offshore atmosphere that are favorable for the occurrence of the offshore-ward migration. In the 27-day period, there are nine days with clear offshore-ward migration. Comparison of the radiosonde data between these nine days and the other eighteen days reveals that strong onshore-ward wind in the boundary layer and offshore-ward wind shear with height aloft in the afternoon and early evening seem to be a key condition for the occurrence of the offshore-ward migration. As these conditions are considered favorable for self-replication process of convective systems to generate new convective cells to the offshore side of the old ones, we can say that our findings support an idea that this process is the major physical mechanism for the offshore-ward migration. The offshore-ward wind shear is caused by large-scale wind variability, which might be associated with cold surges over the South China Sea, and the strength of sea-breeze circulation.