Summary: The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [D. Emerson et al., A diffusion gradient chamber for studying microbial behavior and separating micro-organisms. Appl. Environment. Microbiol. (1994)]. Its purpose is to characterize genetic variants that occur in many biological experiments. A mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC.