Ponding at the soil surface exerts profound impacts on infiltration. However, the effects of ponding depth on infiltration, especially the development of a saturated zone below the soil surface, have not been considered in present infiltration models. A new general Green-Ampt model solution (GAMS) was derived for a one-dimensional vertical infiltration into soils under a uniform initial moisture distribution with ponding on its surface. An expression was included in the new solution for simulating the saturated layer developed below the soil surface as long as the pressure head at the surface is greater than the water-entry suction. The GAMS simulates the infiltration processes closer to the numerical solution by HYDRUS-1D than the traditional and a recently improved Green-Ampt model. Moreover, an inversion method to improve the estimates of soil hydraulic parameters from one-dimensional vertical infiltration experiments that is based on the GAMS was suggested. The effect of ponding depth (hp), initial soil moisture content, soil texture, and hydraulic soil properties (Ks, hd and n) in the saturated zone was also evaluated. The results indicate that the saturated zone developed at a much faster rate than the unsaturated zone during infiltration. Generally, a larger saturated zone was found for soils with higher initial soil moisture content, coarser texture, higher Ks values and lower hd and n. Our findings reveal that including the saturated zone in the infiltration model yields a better estimate for the soil hydraulic parameters. The proposed GAMS model can improve irrigation design and rainfall-runoff simulations.