A terahertz detector of GaN/AlGaN high electron mobility transistor (HEMT) with a high speed and a high sensitivity integrated with low-pass filters is fabricated.The experimental study indicates that, when the low-pass filters are added between the terahertz antennas and the lead electrode, the resonance performance of THz coupled antenna is restored. At the room temperature, the responsivity of the device reaches 1.05×103 V·W-1, and the noise equivalent power reaches 4.7×10-11 W when the bandwidth is 1 Hz. This detector unit is used for the fast scanning imaging of different materials, and the results show that this detector unit has a high imaging resolution and its response speed is superior to those of the commercial pneumatic detectors and pyroelectric detectors.