Investigating the dendritic competitive growth mechanism is of great importance for directional solidification, and the numerical simulation technique is regarded as an effective approach to a description of microstructural evolution. Therefore, a modified cellular automaton model with decentered square algorithm is developed for quantitatively simulating the dendritic competitive growth process. The model takes into account the simplified thermal field, solute diffusion, growth kinetics, etc., and the solid fraction increment calculation is achieved through local level rule method. The model is successfully used to describe the dendrites with various growth orientations and its availability in simulating dendritic competitive growth is verified by comparing with the experimental results of transparent alloy. For the nickel-based superalloy, the simulated results reveal that in the case of converging dendrites, the unfavorably oriented dendrite is able to overgrow the favorably oriented dendrite, which is dependent on the preferential growth angle. For the divergence case, the favorably oriented dendrite can overgrow the unfavorably oriented dendrite through side branching at the grain boundary. The competitive growth process is mainly controlled by the pulling rate and the preferential growth angle. Furthermore, the model is successfully extended to the simulation of three-dimensional dendritic competitive growth.