This study aims to control the self-propulsion of 1-pentanol droplets. When 1-pentanol droplets are dropped in an aqueous 1-pentanol solution, droplets move spontaneously. This self-propulsion is due to interfacial tension gradient caused by concentration differences. The shape of the droplet is deeply related to droplet behavior because the shape of the droplet changes the interfacial tension gradient. In this study, an exoskeleton is introduced to fix the droplet shape. In our preliminary experiments, we observed Marangoni convection in droplets dropped in exoskeleton frames with boomerang and round shapes holes. The results showed that a large surface tension difference was necessary to control the self-propulsion of 1-pentanol droplets. In this study, we prepared two exoskeletons having different holes, which have an elongated symmetrical elliptical shape and an asymmetrical shape to fix the shape of the droplet. Then, we dropped droplets into each exoskeleton, and observed the droplet behavior, Marangoni convection inside the droplet, and the convection in the aqueous phase. We found that the direction of self-propulsion of the droplet was determined by these exoskeletons, especially in the case of the asymmetrical exoskeleton, and the direction of self-propulsion was fixed in one direction. Marangoni convection was observed in the droplet from the direction of lower surface tension to that of higher surface tension. In the aqueous phase, two convections were generated from the aqueous phase to the droplet because of the diffusion of 1-pentanol. Especially, when an asymmetrical exoskeleton was used, two convections with different sizes and velocities in aqueous phase were observed. From these experimental results, the relationship between droplet behavior and convection will be discussed.