In this study we used Hydrus-1D to simulate water infiltration from a ring infiltrometer. We generated water content profiles at each time step of infiltration, based on a particular value of the saturated hydraulic conductivity while knowing the other van Genuchten parameters. Water content profiles were converted to dielectric permittivity profiles using the Complex Refractive Index Method relation. We then used the GprMax suite of programs to generate radargrams and to follow the wetting front using arrival time of electromagnetic waves recorded by a Ground-Penetrating Radar (GPR). Theoretically, the depth of the inflection point of the water content profile simulated at any infiltration time step is related to the peak of the reflected amplitude recorded in the corresponding trace in the radargram. We used this relationship to invert the saturated hydraulic conductivity for constant and falling head infiltrations. We present our method on synthetic examples and on two experiments carried out on sand. We further discuss the possibility of estimating two other van Genuchten parameters, n and α, in addition to the saturated hydraulic conductivity.