A generalized trigonometric series function (GTSF) model, with an adjustable number of parameters, is proposed and analyzed to study ionosphere by using GPS, especially to provide ionospheric delay correction for single frequency GPS users. The preliminary results show that, in comparison with the trigonometric series function (TSF) model and the polynomial (POLY) model, the GTSF model can more precisely describe the ionospheric variation and more efficiently provide the ionospheric correction when GPS data are used to investigate or extract the earths ionospheric total electron content. It is also shown that the GTSF model can further improve the precision and accuracy of modeling local ionospheric delays.