The safety valve is the core component of the pressure-relief protection device for pressure-bearing special equipment. When the safety valve leaks, the medium of the pressure vessel will be lost and wasted, which may cause safety accidents. With the aim to solve the problem of accurately locating the multiple leakage sources of safety valves, a localization method combining a uniform circular array acoustic emission detection and an improved multiple signal classification (MUSIC) algorithm is proposed. First, an improved wavelet threshold function denoising method is introduced to extract acoustic emission signals with high SNR, thereby reducing the rank of the covariance matrix, weakening the noise dispersion caused by eigenvalue reconstruction, avoiding signal and noise cross-confusion, and improving positioning accuracy. By introducing a windowed fast Fourier transform (FFT) frequency division processing link to obtain narrowband signal, the premise of using MUSIC positioning algorithm is established. In addition, a forward/backward spatial smoothing algorithm is introduced in the decoherence link to reduce co-channel interference, reduce the rank loss of the signal covariance matrix, and improve the positioning accuracy of the algorithm. The results show that when the working pressure is 0.70 MPa, 0.75 MPa, and 0.80 MPa, the deviation between the azimuth angle and elevation angle positioning results of each leakage source obtained by the improved MUSIC algorithm and the actual angle does not exceed 2°, and the relative error does not exceed 3.5%. Therefore, the improved MUSIC algorithm can accurately locate multiple leakage sources of the safety valve, and as the working pressure of the safety valve increases, the positioning accuracy of the improved MUSIC algorithm also increases accordingly.