A newly designed terahertz quantum-well photodetector (THz QWP) sandwiched between GaAs and GaAs/Al0.04Ga0.96As material was demonstrated. Experimentally, we measure the response photocurrent spectra and the current-voltage curve and obtain the peak response of 6.78 THz and background-noise-limited performance (BLIP) temperature of 16 K. Theoretically, we investigated the many body effect to the band structure of THz QWP and calculate the peak response of 6.64 THz which is in agreement with the experiment. So, many-body effect must be included in the design of THz QWPs. Then, we calculate the BLIP temperature of 17.5 K which is fitted well with the measurement. However, the low BLIP temperature is the main factor limiting applications of THz QWPs; we propose two schemes to improve the operating temperatures. Firstly, a scheme using an optical antenna to increase the BLIP temperature is proposed. Calculation shows the device is expected to achieve BLIP at 76 K when employing a 106 enhancement antenna. The second scheme is to use a THz quantum cascade laser as signal source to achieve photon-noise-limited performance (PLIP) at high temperatures. Simulations show that when the illumination intensity reaches 0.01 mW/μm2, the operation temperature could be 77 K.