A two-dimensional (2D) lattice Boltzmann method (LBM)-cellular automaton (CA) coupled model is developed for the simulation of dendritic growth and bubble formation during solidification. In the model, the dendritic growth is simulated by a CA approach. The driving force of dendritic growth is determined by a local solute equilibrium approach. The LBM based on the Shan-Chen multiphase flow scheme is adopted to simulate the growth and the motion of bubbles in liquid. The interaction mechanism between dendrites and bubbles is embedded in the model. Model validation is carried out by comparing the simulations with the Laplace law, and by simulating the wettability of a bubble on a smooth solid surface. The proposed model is used to study the effect of gas-liquid interaction coefficient on single bubble growth. It is found that the growth velocity and the equilibrium radius of bubble increase with the gas-liquid interaction coefficient. The simulations of the dendritic growth and bubble formation during directional solidification reproduce the physical phenomena, including dendritic competitive growth, the preferential nucleation locations of bubbles, and bubble growth, coalescence, deformation due to the squeeze of neighboring dendrites, as well as bubble motion in the liquid channels. The simulation results are compared reasonably well with the experimental results. In addition, gas pore volume fraction increases with the initial gas content. The simulations of the present LBM-CA model provide an insight into the physical mechanism of bubble nucleation, growth, and motion, as well as the interaction between the dendritic growth and bubble formation during solidification.