It is important to confirm the accuracy and reliability of commonly used ionosphere models climatologically. In this contribution, International Global Navigation Satellite System Global Ionospheric Maps (IGSG) and two empirical models, that is, NeQuick2 and IRI-2016, are assessed in detail by applying different assessment methods, for example, Jason2/3 ionospheric data, difference of Slant Total Electron Content (dSTEC) data derived from Global Navigation Satellite System (GNSS) phase observation, and single-frequency precise point positioning. Compared with IGSG, the biases mainly range from −10 to 10 Total Electron Content Unit (TECU), while they are between −5 and 5 TECU on solar low-level days for empirical models. The hourly mean biases are about −2.7 and −2.5 TECU for IRI-2016 and NeQuick2 models, respectively. Over the oceanic region, the mean biases for IRI-2016 and NeQuick2 models relative to Jason2/3-Vertical Total Electron Content (VTEC) are smaller than that of IGSG. The Root Mean Square (RMS) values are 4.8 and 6.0 TECU for IGSG and empirical models relative to Jason2-VTEC while the values are 5.4 and 6.0 TECU with relative to Jason3-VTEC. Compared with dSTEC values derived from the selected stations, the RMS values are about 1.8 and 2.6 TECU for IGSG and empirical models, respectively. In the positioning domain, the accuracy of single-frequency precise point positioning corrected by the three models can reach 1 m in three-dimensional direction. The positioning accuracy is 0.17 m corrected by IGSG and 0.50 m corrected by IRI-2016 and NeQuick2 in the horizontal direction.