In this paper, we present the regional ionospheric delay models for Global Navigation Satellite System (GNSS). An ionospheric delay is a dominant error on GNSS positioning. Then, an ionospheric delay should be corrected for a high positioning accuracy. In this study, the methods to develop the ionospheric delay models are proposed. Ionospheric delays can be measured by the geometry-free combination of the GNSS regression (GR) models of dual frequency bands. An ionospheric delay is proportional to total electron content (TEC) and then a vertical component of TEC (VTEC) is modeled. The VTEC models have been developed based on spherical cap harmonic analysis (SCHA) by using GNSS earth observation network (GEONET) data. The GEONET data are observed only in Japanese region and provided by the Geospatial Information Authority of Japan (GSI). We also investigate the prediction of ionospheric delays with the post-processing models developed by the SCHA. We propose the prediction methods by periodic autoregressive (PAR) models.