We present a two-dimensional depth-averaged numerical model simulating reactive transport in shallow water domains subject to given flow conditions. A new approach is used to account for more conceivable kinetically-controlled chemical reactions than have been included in previous models. In this model, a chemical may dissolve in the water column or in the interstitial water of the bed sediments, react with other dissolved chemicals to form new chemicals also in the dissolved phase, or be sorbed onto sediments to become particulate chemicals. To save computer time, we employ a predictor-corrector strategy to deal with the reactive transport equations of mobile substances where transport equations are computed in the predictor step with reaction rates estimated at the previous time step, and rate correction is achieved node by node in the corrector step to obtain the concentration distributions at the present time step. For immobile substances, we solve the corresponding ordinary differential equations together with the corrector equations of mobile substances in the corrector step by using the Newton-Raphson method. Two examples are demonstrated to show the capability of our model.