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This study focuses on the dynamic behavior of rising bubble in water with taking surface tension and viscous effect into consideration. The Young-Laplace equation is adopted to obtain the viscous component of the normal stress, and the tangential component is evaluated by viscous correction pressure, which is based on viscous dissipation energy equivalence principle. Firstly, both axi-symmetric and three-dimensional model is established by employing boundary integral method. The validation of our model is confirmed by comparing the analytical results with the experimental results, and they are in good agreement with each other. Secondly, the shape and balanced velocity of millimetre-sized bubble are studied, and the influences of initial condition, surface tension and viscosity on the dynamic behaviour of the bubble are also discussed. Finally a numerical technic is put forward to handle the coalescence of two rising bubbles, which can show some detailed information about the coalescence process.