A magneto-metasurface with nonreciprocal terahertz (THz) transmission has been proposed to form a THz isolator. Importantly, we have discussed the two necessary conditions for THz nonreciprocal transmission in the metasurface: (1) There should be magneto-optical responses for THz waves in the metasurface; (2) The transmission system of the metasurface needs to be asymmetric for forward and backward waves. These two conditions lead to the time reversal symmetry breaking of system, and the magnetoplasmon mode splitting and nonreciprocal resonance enhancement can be observed in the asymmetry magneto-metasurface. Moreover, the isolation dependences and tunability on the external magnetic field and temperature have also been investigated, which shows that the best operating state with a high isolation can be designed. The numerical simulations show a maximum isolation of 43 dB and a 10 dB operating bandwidth of 20 GHz under an external magnetic field of 0.3 T, and the insertion loss is smaller than 1.79 dB. This low-loss, high isolation, easy coupling THz isolator has broadly potentials for THz application systems.