The speckle noise in the imaging process of medical ultrasound imaging will be mixed with effective information, which will reduce the image quality and affect the doctor's diagnosis. Therefore, it is of great significance to study the denoising method of medical ultrasound images. Guided image filtering is a kind of edge-preserving algorithm, which can smooth the image at the same time reserving the edge of the image. However, because guided image filtering is insensitive to texture details, it can result in the loss of detailed information of the medical ultrasound image, and the fractional differential method can just compensate for this disadvantage. In order to reserve the edge features and texture features of medical images while removing noise, we propose a denoising method of medical ultrasound image based on guided image filtering and fractional derivative. Firstly, we logarithmically transform medical ultrasound images so the multiplicative noise is convert into additive noise. Then, in order to retain the detailed information of the medical ultrasound image, it is necessary to enhance its sensitivity to the texture details of the guide filter. In this paper, the image is processed with a fractional differential mask to obtain enhanced texture information, which is then imported into the guided image filter. Next, the medical ultrasound image is processed using the guided image filter containing texture information, and finally an exponential transformation is performed to obtain a denoised image. Through experiments, we can conclude that the proposed algorithm not only can effectively enhance the visual effects of ultrasound images while removing noise, but also can effectively preserve edge and texture information.