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In order to improve the accuracy and effectiveness of traditional image denoising algorithms, this paper combines the characteristics of medical images and addresses the problem of insufficient edge and detail information preservation capability in the traditional anisotropic diffusion speckle reducing algorithm (SRAD). A wavelet analysis-based anisotropic diffusion speckle reducing algorithm (Wavelet-SRAD) is proposed. Using Matlab for simulation experiments, the proposed algorithm is compared with traditional median filtering, Gaussian filtering, mean filtering, and SRAD filtering algorithms. Mean, standard deviation, speckle index, and equivalent visual number are calculated to analyze the denoising results. The denoising effect is visualized from the energy perspective using a grayscale histogram. The experimental results show that compared with traditional image filtering denoising algorithms, the improved Wavelet-SRAD algorithm can more accurately and effectively remove speckle noise in medical ultrasound images, and has good preservation capability for tissue texture and edge detail information, demonstrating superior filtering and denoising performance. Therefore, the improved Wavelet-SRAD filtering denoising algorithm is an effective method for suppressing speckle noise in medical ultrasound images.