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To investigate the coupling relationship between earthquake and ionosphere perturbation, we process the global total electron contents (TECs) estimated from GPS data of IGS stations by CODE and analyze TEC anomalies before M 8.6 Sumatra earthquake and M 6.7 Mexico earthquake on April 11, 2012. The sliding interquartile method with the sliding window of 27 days is used to process data of SSN, F10.7 solar flux, Dst and Kp to eliminate the effects of solar activity and the geomagnetic activity. The results show that there are positive and negative TEC anomalies over epicenter on the 11th day and the 3rd day prior to the Sumatran earthquake respectively. But the decrement and increment of TEC anomalies over epicenter occurred on the 11th day and the 3rd day prior to the Mexico earthquake. The global TEC anomalies are analyzed on the 11th day and the 3rd day before these two great earthquakes, respectively. The magnitudes of TEC anomaly occurred on the 3rd day before earthquakes are larger than that occurred on the 11th day before earthquakes. This indicates the magnitude of anomaly may be related to the number of days prior to earthquake. But the magnitude of TEC anomaly near Sumatran is lower than that near Mexico, and the duration of anomalies occurred on 11th day is longer than those on 3rd day prior to earthquake, which are different from previous results. The TEC anomaly of Sumatran earthquake mainly occurs in the afternoon and night local time, but the TEC anomaly of Mexico earthquake mainly occurs in the morning local time. The TEC anomaly peak regions before these two earthquakes appeared on the south of epicenters instead of the vertical projection of the epicenter. Corresponding ionospheric anomalies are also observed in the magnetically conjugated regions. These can be guidance for the ionosphere monitoring in earthquake study. [ABSTRACT FROM AUTHOR]