In order to take full advantage of the high electron mobility of the AlGaN/GaN high-electron-mobility transistor (HEMT) terahertz detector array, the detection characteristics of the HEMT terahertz detector array at 77 K are studied. A low temperature system suitable for the focal-plane array (FPA) chip is built based on liquid nitrogen Dewar. Comparison tests of the FPA at room temperature and low temperature is realized. When the temperature is lowered from 300 K to 77 K, the average responsivity of the detector array pixels increase by about 3 times, the average noise increases slightly, and the average noise-equivalent power (NEP) is reduced from 45.1 pW/Hz^1/2 to 19.4 pW/Hz^1/2 at 340 GHz, i.e., the sensitivity is more than doubled. Compared with the single detector coupled with silicon lens, there is still a lot of room for improving the sensitivity of array pixels. It is mainly due to the inconsistency of the optimal working voltage of each pixel, that leads to a large dispersion of the responsivity and noise between pixels under a given unified working voltage. Possible solutions to the problem of inconsistent optimal working voltage are discussed in this paper.