According to practical geological and hydrogeological conditions of riverside water-supply well fields in northwestern China, an ideal hydrogeological model has been generalized and a three-dimensional mathematical model has been set up. A finite difference method was applied to simulating groundwater flow near a partially penetrating river under riverside pumping, and to analyzing the effects of river width, partial penetration and permeability of riverbed sediments on groundwater recharges. Results show that riverside pumping may cause groundwater to flow beneath the partially penetrating river, and that river width, penetration and riverbed permeability obviously influence flows from the partially penetrating river and constant-head boundaries. However, the pumping output is mainly from the partially penetrating river.