Bubble rising phenomenon is widely found in many engineering applications including stream generators in power plants. Many experimental and numerical researches have been performed to predict the dynamic behavior of the bubble rising process. Most simulations so far have focused on evolution behavior of the rising bubble itself. Rising bubbles could penetrate through the top free surface which makes the problem much more complicated in addition to the curvature effect on the interface. With top surface, satellite droplets may be generated near breakup region and entrained to rising velocity field. In this paper, the effect of top free surface on rising bubble has been numerically investigated. High-order tetra-marching level contour reconstruction method (LCRM), which is a hybridization of front-tracking and level-set methods has been used to track the gas-liquid interface explicitly. Effects of free surface on the interfacial shape and behavior after breakup are studied with different size and depth of the initial bubble. It has been found that the initial diameter of the bubble is the dominant factor controlling the satellite droplet formation.