In this study, we employ far-field GPS total electron content (TEC) observed in Hawaii to detect the ionospheric disturbances induced by the 2011 Tohoku tsunami. We observed tsunami-driven traveling ionospheric disturbances (TIDs) at two different times: at about 12:40 UT, there were TIDs in the disturbance series propagating at approximately 260 m/s in an outward direction from the tsunami's source, and then, the signals began to weaken and gradually disappeared after 14:00 UT; however, at about 17:30 UT, the TIDs appeared again in the disturbance series with similar propagation characteristics. According to the observation times, the former TIDs can be attributed to the straight tsunami from the mainshock, while the latter TIDs are most likely driven by tsunami from aftershocks. Furthermore, we also observed tsunami-like TIDs at about 11:50 UT with similar horizontal velocity and direction compared to tsunami waves. However, the arrival time of the TIDs was about 1.5 earlier than tsunami waves in the sea level and should be induced by other sources.