This study aims to analyze the convection flow generated three-dimensionally around and inside a 1-pentanol droplet dropped into a 1-pentanol aqueous solution. The difference in concentration between the droplet and the aqueous solution causes an interfacial tension gradient, and then the droplet starts moving in the aqueous solution. The droplet shape is closely related to its self-propulsion behavior because the interfacial tension gradient changes with the droplet shape. In this study, we fix the droplet shape using an exoskeleton to control the self-propulsion direction. The exoskeleton is fabricated by using OHP film with a circular-shape having a hole in the center, and a droplet is dropped into the hole to fix the droplet shape. We prepared two different exoskeletons having symmetrical elliptical holes and asymmetrical elliptical holes. We also prepare two different concentrations of aqueous solutions. By using two different concentrations of aqueous solution and two types of exoskeletons, we analyze the behavior of the droplet dropped into the exoskeleton hole, in relation with the convection around and inside the droplet. The results indicate that the self-propulsion direction of the droplet is determined by the shape of the droplet, which is fixed by the exoskeleton. Particularly in the case of the asymmetrical exoskeleton, the self-propulsion direction is fixed in one direction. The self-propulsion velocity of the droplets changed depending on the concentration of the aqueous solution, and we observed the droplet to self-propel several times per 50 seconds when the aqueous solution of smaller concentration was used. Based on these experimental results, we discuss the dominant factors to determine the self-propulsion direction by visualizing the convection around and inside the droplet.