This paper describes an ionospheric correction technique for single frequency GPS measurements from satellites in low Earth orbit. The fractional total electron content (TEC) above the receiver altitude is obtained from global TEC maps of the International GPS Service network and an altitude dependent scale factor. By choosing a suitable effective height of the residual ionosphere, the resulting path delay for positive elevations is then computed from a thin layer approximation. The scale factor can be predicted from the assumption of a Chapman profile for the altitude variation of the electron density or adjusted as a free parameter in the processing of an extended set of single frequency measurements. The suitability of the proposed model is assessed by comparison with flight data from the Champ satellite that orbits the Earth at an altitude of 450 km. For the given test case, a 90% correction of the ionospheric error is achieved in a reduced dynamic orbit determination based on single frequency C/A-code measurements.