The AlGaN/GaN-based sensor is a promising POCT (point-of-care-testing) device featuring miniaturization, low cost, and high sensitivity. BNP is an effective protein biomarker for the early diagnosis of HF (heart failure). In this work, a novel AlGaN/GaN device with the Kelvin connection structure and the corresponding detection technique was proposed. This technique can effectively suppress the background noise and improve the SNR (signal-to-noise ratio). A BNP detection experiment was carried out to verify the effectiveness of this technique. It is shown that compared with that of the traditional detection method, the LOD (limit of detection) was improved from 0.47 ng/mL to 1.29 pg/mL. The BNP detection experiment was also carried out with a traditional electrochemical Au-electrode sensor with the same surface functionalization steps. The AlGaN/GaN sensor showed a better LOD than the Au-electrode sensor. Moreover, the influence of AlGaN/GaN sensor package on background noise was investigated with the mechanism of the noise source revealed. Finally, based on the optimized package, the optimal SNR quiescent operating point of the AlGaN/GaN sensor was determined. By biasing the sensor at the optimal quiescent operating point and immobilizing the magnetic beads with anti-BNP on the gate of the AlGaN/GaN sensor, the LOD for BNP detection was further improved to 0.097 pg/mL.