We have developed a numerical simulation code to solve multi-phase flow with mass transfer through interfaces. Each phase is treated as a part of one fluid with locally different density and viscosity. The incompressible NS(Navier-Stokes) equation is solved by a FVM(finite volume method) adopting the MAC-type algorithm. The position of the interface is determined by solving a transport equation of MDF(marker density function). Surface tension is transformed to the body force in the NS equation by using the porosity concept. Here we consider that mass is dissolved from a dispersed phase, which forms droplets, into a continuous phase. Outside of droplets, we solve a advection-diffusion equation for the transfer of the dissolved mass. Assuming that the mass is saturated at the interface, diffusion flux is considered through the interface as the boundary condition for mass transfer. It is also used to calculate the diminishing rate of the volume of the dispersed phase. After checking the accuracy of this dissolution algorithm by solving an ideal case having an analytical solution, we applied this method to the dissolution from a rising droplet. It is visualized numerically that the dissolved mass attaches horse-shoe type vortices in the wake of the deformed rising droplet.