This paper theoretically studies the high-electron-mobility transistor (HEMT) driven by the terahertz radiation.It calculates the gate-to-source/drain admittance and the detection responsivity of the HEMT as a function of the signal frequency.It finds that the peaks of the admittances and the responsivity show redshift,and the heights of the peaks decrease with increasing the lengths of the source-to-gate and gate-to-drain spacing.Such phenomena may be useful in designing different HEMTs by utilizing the effects associated with the plasma oscillations excitation.