This work describes an enhanced corona triode with constant current adapted to characterize the electrical properties of thin dielectric films used in organic electronic devices. A metallic grid with a high ionic transparency is employed to charge thin films (100 s of nm thick) with a large enough charging current. The determination of the surface potential is based on the grid voltage measurement, but using a more sophisticated procedure than the previous corona triode. Controlling the charging current to zero, which is the open-circuit condition, the potential decay can be measured without using a vibrating grid. In addition, the electric capacitance and the characteristic curves of current versus the stationary surface potential can also be determined. To demonstrate the use of the constant current corona triode, we have characterized poly(methyl methacrylate) thin films with films with thicknesses in the range from 300 to 500 nm, frequently used as gate dielectric in organic field-effect transistors.