Droplet evaporation by a localized heat source under microgravity conditions was numerically investigated in an attempt to understand the mechanism of the fuel vapor jet ejection, which was observed experimentally during the flame spread through a droplet array. An Eulerian-Lagrangian method was implemented with a temperature-dependent surface tension model and a local phase change model in order to effectively capture the interfacial dynamics between liquid droplet and surrounding air. It was found that the surface tension gradient caused by the temperature variation within the droplet creates a thermo-capillary effect, known as the Marangoni effect, creating an internal flow circulation and outer shear flow which drives the fuel vapor into a tail jet. A parametric study demonstrated that the Marangoni effect is indeed significant at realistic droplet combustion conditions, resulting in a higher evaporation constant. A modified Marangoni number was derived in order to represent the surface force characteristics. The results at different pressure conditions indicated that the nonmonotonic response of the evaporation rate to pressure may also be attributed to the Marangoni effect.