A terahertz quantum well photodetector (THz-QWP) is designed and the many-body effect is investigated in this device. By characterizing and analyzing the photo-current spectrum of this device, it is found that the many-body effect changes the peak response frequency and causes the phenomenon of two response peaks, and thus it is confirmed that the many-body effect can deepen the depth of the effective well potential and simultaneously increase the energy spacing between the first excited state and the ground state. Therefore, it is important for the THz-QWP design to take the many-body effect into account.