A three-dimensional ionospheric electron density (N e) model has been named the TaiWan Ionospheric Model (TWIM) and constructed from monthly-weighted and hourly vertical Ne profiles retrieved from FormoSat3/COSMIC GPS radio occultation (RO) measurements. The TWIM exhibits vertically-fitted α-Chapman-type layers, with distinct F2, F1, E, and D layers, and surface spherical harmonics approaches for the fitted layer parameters including peak density, peak density height, and scale height. These results are useful in investigation of near-Earth space and large-scale N e distribution. This way the continuity of N e and its derivatives is also maintained for practical schemes for providing reliable radio propagation predictions. We also present a numerical and step by step ray-tracing method on the TWIM. With the Earth's magnetic field and horizontal N e gradient effects included, efficient methods for calculating ray parameters such as phase path and group path are presented. The methodology has been successfully applied to a practical high-frequency transmitter for oblique incidence ray tracing and further evaluated by comparing synthetic vertical ionograms generated by the method with experimental ionosonde observations. Furthermore, the ray-tracing methodology also has potential applicability to ionospheric correction as applied to single frequency GPS receivers. In this paper, ionospheric delay correction for single-frequency GPS pseudoranges using the TWIM is presented. Its performance with respect with the ionospheric correction using other ionospheric model and the dual-frequency GPS receiver will also be presented.