Two-dimensional principal component analysis (2DPCA) was performed to examine ionospheric 2D total electron content (TEC) variations obtained from the NASA Global Differential GPS (GDGPS) network, which consisted of low spatial resolution ionospheric TEC data, to detect TEC precursors prior to the China Ludian earthquake at 08:30:13 UT on 03 August 2014 (M = 6.1). Results have shown that two TEC precursors were observed three days prior to this earthquake. The characteristics of all principal eigenvalues were considered to determine the TEC precursors of the earthquake in this study. This study aimed to differentiate the previous studies of Lin about PCA and 2DPCA using only the characteristic of the first principal eigenvalue to determine the TEC precursors of the earthquake. However, some other TEC precursors could be lost in processes that do not analyze characteristics of other principal eigenvalues. Therefore, this research can be considered as a full analysis that examined the detailed surrounding TEC precursors of the earthquake and could be treated as a new study scope. The TEC precursor during 06:15 to 06:20 (UT) on 01 August 2014 localized near the epicenter was more intense compared with the characteristic of the first largest principal eigenvalue. However, another localized TEC precursor from 06:15 to 06:20 (UT) on 01 August 2014 was found to be more intense, which was far from the epicenter east of the first largest principal eigenvalue. The more plausible reason for the two TEC precursors could be the density variances caused by radon-gas release due to the fine crack stress transfer from the rocks according to Coulomb stress transfer theory as applied to a far TEC precursor. The durations of both TEC precursors were at least 5 min. This research could be treated as a full and detailed examination of surrounding TEC precursors.