In the present study, we developed a three-dimensional numerical method based on the level set method that can be applicable to the two-phase systems with high-density ratio. In the level set method, we must reinitialize the level set function to keep the level set function as a true distance function. To achieve the perfect mass conservation of two fluids systems, we modified the reinitialization procedure developed by Sussman et al. We simulated the coalescence of two rising bubbles under gravity to evaluate the mass conservation for the present method. We succeeded in simulating the bubble coalescence when the density ratio between the gas and the surrounding liquid is 0.001. It is shown that the mass conservation of bubbles is very well even after the bubble coalescence.