The detection of weak acoustic waves excited by partial discharge (PD) in oil-paper insulation is considered as a critical challenge in transformer condition monitoring, while existing high-sensitivity acoustic sensing methods are constrained by the low signal-to-noise ratio (SNR) of the acoustic waves. In this paper, an acoustic enhancement detection method based on gradient acoustic metamaterial (GAM) is proposed, achieving compression and amplification of broadband acoustic waves and providing a solution for improving the SNR of weak PD acoustic signals. The GAM is constructed using 30 circular plate units with diameters increasing according to a quadratic function. The thickness of each unit is 1 mm, the gap distance is 1 mm, the minimum diameter is 5 mm, and the maximum diameter is 47.05 mm, with the overall structure's maximum size being less than 6 cm. Numerical calculations of the acoustic pressure amplification effect of the GAM reveal that although the gain factor is reduced by the limited acoustic impedance difference between the GAM and the insulating oil, the amplification bandwidth is broadened, enabling the enhancement of broadband PD acoustic signals. By integrating the acoustic sensor with the end unit of the GAM, narrow-gap acoustic field detection and structural integrity of the GAM are simultaneously achieved, and the enhancement effect of the GAM in insulating oil is demonstrated experimentally. A gain effect is exhibited by the GAM in the frequency range of 45 kHz to 200 kHz, with a peak gain factor exceeding 3. Finally, the results of needle-tip PD show that the detected acoustic wave peak is directly enhanced by the GAM, and the frequency content within the GAM amplification band is significantly improved, thus achieving enhanced detection of PD acoustic waves. This study represents acoustic metamaterials to enhance acoustic detection, which is considered highly significant for the early detection of PD.