We can observe the changes of Total Electron Content, TEC, in ionosphere by analyzing the data from Global Navigation Satellite Systems (GNSS) satellites. Up to now, preseismic TEC anomalies have been reported in several papers. However, they are not so clear as coseismic TEC anomalies, and their analysis methods have some problems for practical earthquake prediction. One factor making it difficult to detect TEC anomalies is large noises in TEC data. Nonnegligible TEC disturbances are caused by many natural mechanisms. To overcome this difficulty, we propose correlation analyses between one GNSS station and GNSS stations surrounding it. First, we model TEC time series over a few hours using polynomial functions of time. Second, we calculate prediction errors as the departure of the TEC time series from the models over time scale of a few minutes and define it as the TEC anomaly. Third, we calculate the correlation between anomaly of one GNSS station and those at the surrounding stations. Although such a correlation method has long been used for radio communications, in particular for spread spectrum communications and very long baseline interferometry to increase signal-to-noise ratio, it has not been widely applied for TEC analysis. As a result of our method, we demonstrate that the correlation analysis can detect preseismic anomalies about 1h before the 2011 Tohoku-Oki earthquake on 11 March (M(w)9.0), 20min before the foreshock on 9 March and 40min before the aftershock on 7 April (M(w)7.3).