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We demonstrate that the tunneling magnetoresistance (TMR) can be used to modulate terahertz (THz) wave propagation through a magnetic tunnel junctions (MTJ). Operating at the THz frequency range, a maximal modulation depth of 60% is reached for the parallel state of the MTJ with the thickness of 77.45 nm, by using a small magnetic field of 30 mT. The THz conductivity spectrum of the MTJ is governed by the spin-dependent electron tunneling. This findings open that the MTJ device will have potential applications in THz magnetic modulators, filtering and sensing.