This study presents a new numerical model for transient shallow groundwater table in an unconfined sloping aquifer considering rainfall recharge. The infiltration is neglected as only a thin sloping aquifer is considered. The theory for groundwater table evolution is the hydraulic groundwater theory, or called Dupuit-Boussinesq theory. The relaxation approach is applied for numerically calculating the nonlinear advection-diffusion equation with the help of the Godunov based finite volume scheme. The transient numerical model is verified with the steady-state solution. We performed two case studies considering variable rainfall patterns and variable aquifer hydraulic conductivity. The resultant hydrographs of outflow discharges and groundwater tables at the downstream outlet are obtained. The results verify that our transient model is practical for modelling motion of thin groundwater table in an unconfined sloping aquifer under variable rainfall patterns.