Flow and transport processes in soil and rock play a critical role in agricultural non-point source pollution (ANSP) loads. In this study, we investigated the ANPS load discharged into rivers from an irrigation district in the Tibetan Plateau, and simulated ANPS load using a distributed model involving detailed descriptions of flow and ANPS transport and transformation processes in the soil and rock. Experiments were conducted for two years to measure soil water content and nitrogen concentrations and the quality and quantity of lateral flow in the rock and at the drainage canal outlet during the highland barley growing period. A distributed model, in which the subsurface lateral flow was described using a step-wise method, was developed to simulate flow and ammonium nitrogen and nitrate nitrogen transport. Sobol’s method was used to evaluate the sensitivity of simulated flow and transport processes to model inputs. The results showed that, with a 21.2% increase of rainfall and irrigation in the highland barley growing period, the average NH4+-N and NO3--N concentrations in the soil layer decreased by 10.8% and 14.3%, respectively, due to increased deep seepage. Deep seepage of rainfall water accounted for 0–52.4% of total rainfall, whereas deep seepage of irrigation water accounted for 36.6–45.3% of total irrigation. NH4+-N and NO3--N discharged into the drainage channel represented 19.9–30.4% and 19.4–26.7% of the deep seepage, respectively. The mean Nash-Sutcliffe coefficients, root mean square errors, and cumulative deviations between the measured and simulated flow rates and NH4+-N and NO3--N concentrations at the surface drainage canal outlet were 0.694, 0.081, and 0.242, respectively, indicating that the proposed method can effectively describe the hydrological and ANPS pollution migration in the plateau irrigation zone. The Sobol’ sensitivity analysis results demonstrated that subsurface lateral flow had the most important first order and total effect on the simulated flow and NH4+-N and NO3--N concentrations at the surface drainage outlet.