Electron irradiation of water ice is an important process in the Solar System, especially for the icy satellites with tenuous atmospheres which are originated from the outgassing of their icy surfaces. In the literature, extensive laboratory experiments have been reported on the electron irradiation on ice to study the chemical compositions (e.g., H2O2) that are formed inside the ice, with volatile gases (e.g., H2 and O2) readily leaving the surface. Meanwhile, semi-empirical models have also been developed to estimate the production of the species of interest in the ice during irradiation as functions of electron energy and ice temperature. In this study, we build the first chemical-transport model to realistically simulate the chemical processes occurring in the ice during electron irradiation and to describe how different chemical species are formed, transported, and distributed in the ice. The simulated H2O2 mixing ratio of our model agrees well with the experiment work performed by Hand and Carlson (2011). Our model can be applied to the icy surfaces of the icy satellites (e.g., Europa) to estimate the oxidant generation in the ice and to evaluate the potential habitability of those satellites. This study inspires further experimental studies about the gas-ice interactions in the future to constrain the crucial parameters in the model.