Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient.