In this paper, we make a theoretical investigation of the plasma-wave instability mechanism in a two-dimensional electron fluid in a high electron mobility transistor (HEMT) driven by the terahertz radiation in the presence of a perpendicular magnetic field. It is found that the resonant peaks of the gate-to-source/drain admittances and detection responsivity depend on the strength of the exteal magnetic field. Such phenomena can be used to produce a desired effect by adjusting the intensity of the magnetic field.