In this work, the rising of a single bubble in a quiescent liquid under Microgravity condition was simulated. In addition to general studies of Microgravity effects, the initiation of hydrodynamic convection, solely due to the variations of interface curvature (surface tension force) and thus the generation of shearing forces at the interfaces was also studied. Then, the variation of surface tension due to the temperature gradient (Marangoni convection), which can initiate the onset of convection even in the absence of buoyancy, was studied. The related unsteady incompressible full Navier-Stokes equations were solved using a finite difference method with a structured staggered grid. The interface was tracked explicitly by connected marker points via a hybrid front capturing and tracking method. A one field approximation was used where one set of governing equations is only solved in the entire domain and different phases are treated as one fluid with variable physical properties, while the interfacial effects are accounted for by adding appropriate source terms to the governing equations. Also, a Multi-grid technique, in the context of the projection method, improved convergences and computational stiffness. The results show that the bubble moves in a straight path under Microgravity condition, compared to the zigzag motion of bubbles in the presence of gravity. Also, in the absence of gravity, the variation of surface tension force due to interface curvature or temperature gradient can still cause the upward motion of the bubble. This phenomenon was explicitly shown in the results of this paper.