A tunable metal/magneto-optic plasmonic lens for terahertz isolator is demonstrated. Based on the magneto-optical effect of the semiconductor material and non-symmetrical structure, this plasmonic lens has not only the focusing feature but also nonreciprocal transmission property. Moreover, a transmission enhancement through this device greatly larger than that of the ordinary metallic slit arrays is contributed by the extraordinary optical transmission effect of the magneto surface plasmon polaritons. The results show that the proposed isolator has an isolation bandwidth of larger than 0.4THz and the maximum isolation of higher than 110dB, and its operating frequency also can be broadly tuned by changing the external magnetic field or temperature. This low-loss, high isolation, broadband tunable nonreciprocal terahertz transmission mechanism has a great potential for terahertz application systems.