We report a Kelvin-probe method to investigate the lateral charge-transport properties of semiconductors, most notably the charge-carrier mobility. The method is based on successive charging and discharging of a pre-biased metal-insulator-semiconductor stack by an alternating voltage applied to one edge of a laterally confined semiconductor layer. The charge carriers spreading along the insulator-semiconductor interface are directly measured by a Kelvin-probe, following the time evolution of the surface potential. A model is presented, describing the device response for arbitrary applied biases allowing the extraction of the lateral charge-carrier mobility from experimentally measured surface potentials. The method is tested using the organic semiconductor poly(3-hexylthiophene), and the extracted mobilities are validated through current voltage measurements on respective field-effect transistors. Our widely applicable approach enables robust measurements of the lateral charge-carrier mobility in semiconductors with weak impact from the utilized contact materials.