In present paper the Inamuro Model based on free energy approach of the Lattice Boltzmann Method (LBM) was used to simulate the motion of bubble and coalescence of two bubbles under buoyancy force. By combining the Tanaka and Inamuro models, three-dimensional model of Inamuro was used in two-dimension for decreasing the computational cost. Firstly it was ensured that the surface tension effect and Laplace low for two density ratio 50 and 1000 were properly implemented. Secondly in next step, effect of governing dimensionless numbers problem such as Etvos number and Morton number on Reynolds number and terminal shape of bubble were investigated. Different flow patterns in various dimensionless numbers were obtained and by changing the dimensionless number, terminal change of bubble’s shape was seen. Finally, motion of two bubbles and terminal shape of coalescence of two bubbles were studied in different dimensionless number, which shape of first bubble was same to single bubble, but it was seen that second bubble experienced various shapes due to its location in wake of first bubble and less difference pressure on two sides of this bubble.