In this work, a two dimensional CFD model has been used to investigate both hydrodynamics and mass transfer and their effects on hydrogen solubility in a hydrocarbon fuel. This work has been done based on two fluid (Eulerian-Eulerian) model and finite volume method, along with standard k-e model to address turbulent behavior of both phases. The bubble rise velocity obtained using the present model has been compared with the experimental results and showed a good agreement with experimental data. The CFD model correctly exhibited the general behavior expected from hydrodynamics of the system. For gas superficial velocities up to 3.0 cm/s, the gas volume fraction and volumetric mass transfer coefficient were obtained up to 0.091 and 0.054 s-1, respectively. Results of mass transfer run showed that hydrogen concentration in liquid fuel is increased progressively until reaching its equilibrium value. For hydrogen mass transfer coefficient of 0.0004, 0.0008 and 0.002, the time required to reaching the equilibrium liquid concentration is about 120, 60 and 25 sec. respectively. Therefore, through selection of an appropriate system geometry and gas velocity, an appropriate mass transfer and gas distribution in liquid for hydrogen solubility in liquid fuel can be achieved.