The rise and mass transfer process of bubbles in a liquid presents a non-equilibrium and strong-coupling characteristic.To predict this process more accurately，a transient acceleration model of bubbles was obtained according to the analysis of forces，especially the Basset force on a rising bubble.Meanwhile，a model for transient and non-equilibrium mass transfer of bubbles was formulated based on the boundary layer mass transfer model around a sphere and non-equilibrium mass transfer theory.These two models were coupled with the gradient of bubble mass to describe the whole rising and mass transfer process of bubbles.Two examples presented showed that the Basset force and non-equilibrium mass transfer would lead to different calculation results for soluble and sparingly soluble bubbles.The calculated values were in better agreement with the experimental data of sparingly soluble bubbles，by utilizing the non-equilibrium mass transfer theory in the coupling model.