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In this paper, the convection-diffusion process in a two-phase air-water flow is investigated. Two-phase flows of air and water are important and are widely used in the industrial applications. Simulation of such a flow needs a proper understanding of the interface between two phases where these is a change in fluids properties. Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian and meshless method which can simply detect the interface of multiphase flows. Here, we develop the open-source SPHyiscs2D code into two phase and implement the convection-diffusion equation by looking carefully at surface tension forces. To validate, first the still-water problem is investigated to ensure that the hydrostatic pressure at the interface is predicted and then the dam-break problem on an infinite bed is compared with the available experimental data. Results show that the combination of surface tension formulations and an additional artificial force gives a better result. Finally, the convection-diffusion process and the concentration distribution are shown for the air-bubble rising problem for different diffusive coefficients. It will be shown that the SPH method is a useful tool for studying multiphase flows and convection-diffusion processes.